Kid Einsteins · Class Pack · Class 14 · Grades 3–4
Kid Einsteins Class 14: Area, Perimeter & Word Problems — 8 SOMATH Posters, Theory & 40 Practice Questions
A complete, illustrated grade 3–4 walk through perimeter, area, area vs perimeter units, area of a square, composite (L- and T-shaped) figures, missing sides, real-life fence-vs-paint word problems, and same-perimeter/different-area comparisons. Eight SOMATH posters, full theory under each one, 40 practice questions, and 20 homework questions with click-to-reveal solutions. Class 14 of the SOMATH Kid Einsteins 48-class rolling syllabus — Upper West Side, NYC.
· By SOMATH · Class 14 of the Kid Einsteins rolling syllabus · (646) 668-6151 · 226 W 79th St, New York, NY 10024
Short answer
Perimeter is the distance around a shape — add every side, and the answer is in regular units (cm, in, ft, m). Area is the space inside — for a rectangle it's length × width, and the answer is in squared units (cm², in², ft², m²). In word problems: fence, ribbon, border, trim mean perimeter; paint, carpet, tile, grass mean area.
Download the student workbook (PDF)22 pages · Cover, eight lesson images, 40 practice questions, eight homework review questions, and 12 homework word problems.Each image is followed by its five questions. Blank answer space; exercise answers are not included.
1. Perimeter — add every side
Poster 1 of 8 — Kid Einsteins Class 14
What is perimeter?
Perimeter is the total distance around the outside of a shape. It is a length. If you walked all the way around a rectangular playground, the perimeter is how far you walked.
To find perimeter, add every side. For a rectangle with length 8 cm and width 5 cm:
P = 8 + 5 + 8 + 5 = 26 cm
Two shortcuts for a rectangle:
P = 2 × length + 2 × width (because both lengths are equal and both widths are equal)
P = 2 × (length + width) (add first, then double)
The answer to a perimeter question is always in regular length units: cm, in, ft, m, km — never squared units.
5 practice questions with hidden solutions
Q1.1 Find the perimeter of a rectangle that is 7 cm long and 3 cm wide.
P = 7 + 3 + 7 + 3 = 20 cm. (Or P = 2 × (7 + 3) = 2 × 10 = 20 cm.)
Q1.2 A square garden has sides of 6 ft. What is its perimeter?
All four sides are equal. P = 4 × 6 = 24 ft.
Q1.3 The perimeter of a rectangle is 40 cm and the length is 12 cm. What is the width?
P = 2 × (length + width) → 40 = 2 × (12 + w). So 12 + w = 20, which gives w = 8 cm.
Q1.4 A rectangular rug is 10 ft by 4 ft. How many feet of tape do you need to run around its outside edge?
You need the perimeter. P = 10 + 4 + 10 + 4 = 28 ft. You need 28 ft of tape.
Q1.5 A picture frame has an outside perimeter of 60 in. The height is 18 in. What is the width?
P = 2 × (height + width) → 60 = 2 × (18 + w). So 18 + w = 30, which gives w = 12 in.
2. Area of a rectangle — length × width
Poster 2 of 8 — Kid Einsteins Class 14
What is area?
Area is the amount of flat space inside a shape. It is measured by counting how many unit squares fit inside.
For a rectangle, you don't need to count every square — just multiply:
A = length × width
For a 6 cm × 4 cm rectangle: A = 6 × 4 = 24 cm². That's 24 unit squares fitting inside.
Why does the multiplication trick work? The rectangle is 6 squares across and 4 rows tall. That's 6 groups of 4 — a multiplication picture (an array). Kid Einsteins Class 3 (area models for ×7, ×8, ×9) is the same idea used for facts.
The answer is always in squared units: cm², in², ft², m². The little 2 tells you it is an area, not a length.
5 practice questions with hidden solutions
Q2.1 Find the area of a rectangle that is 9 cm long and 5 cm wide.
A = 9 × 5 = 45 cm².
Q2.2 A classroom rug is 8 ft by 6 ft. What is its area?
A = 8 × 6 = 48 ft².
Q2.3 A rectangle has area 36 cm² and width 4 cm. What is its length?
A = length × width → 36 = length × 4. So length = 36 ÷ 4 = 9 cm.
Q2.4 A tablet screen is 10 in long and 7 in wide. How many square inches of screen is that?
A = 10 × 7 = 70 in².
Q2.5 A bedroom floor is 12 ft by 11 ft. How many square feet of carpet cover the floor?
A = 12 × 11 = 132 ft².
3. Perimeter uses regular units. Area uses squared units.
Poster 3 of 8 — Kid Einsteins Class 14
How do I know if a problem is asking for area or perimeter?
Look at the units in the answer — or the units the question expects.
Perimeter is a length. Its units have no little 2: cm, in, ft, m, km.
Area is a flat space. Its units always have a little 2 ("squared"): cm², in², ft², m², km².
The number 2 (called "squared") is a note that says two directions were multiplied — length × width. That's what makes it area.
The word-problem rule
Word problems rarely say "find the perimeter" or "find the area." Instead they ask a real question. Match the object to the idea:
Q3.1 Which is asking for perimeter and which is asking for area? (a) How much fence do we need for a garden? (b) How much grass will cover the yard?
(a) Perimeter — fence goes around the edge. (b) Area — grass fills the inside.
Q3.2 Riley's answer is 24 cm². Did Riley find the perimeter or the area?
The squared unit (cm²) means it's an area.
Q3.3 A rectangular pool is 20 ft by 12 ft. Which value is the pool's perimeter and which is its area? Choices: 64 ft, 240 ft².
Perimeter = 20 + 12 + 20 + 12 = 64 ft. Area = 20 × 12 = 240 ft².
Q3.4 A rug is 6 ft by 4 ft. How much trim tape do we need for the edge, and how much rug fabric is on the floor?
Trim = perimeter = 2 × (6 + 4) = 20 ft. Rug fabric = area = 6 × 4 = 24 ft².
Q3.5 True or false: if a rectangle's dimensions are in feet, then its area is in feet.
False. If the sides are in feet, the area is in square feet (ft²), not feet.
4. Area of a square — side × side
Poster 4 of 8 — Kid Einsteins Class 14
Why does a square get its own formula?
A square is a rectangle where all four sides are equal. So the same rectangle formula still works — it just gets shorter:
A = side × side = s²
For a square with a 5 cm side:
A = 5 × 5 = 25 cm²
The perimeter of a square is easy too, because all four sides are the same:
P = 4 × side = 4 × 5 = 20 cm
The word "squared"
Here's the connection Kid Einsteins should notice: the area of a square is called "side squared." That's where the little 2 in cm² and ft² comes from. Any area is basically "how many little squares fit inside."
5 practice questions with hidden solutions
Q4.1 Find the area of a square with side 7 in.
A = 7 × 7 = 49 in².
Q4.2 Find the perimeter of a square with side 9 cm.
P = 4 × 9 = 36 cm.
Q4.3 A square poster has area 64 cm². How long is each side?
Side × side = 64. The number that multiplies by itself to make 64 is 8. So side = 8 cm.
Q4.4 A square photo has perimeter 40 cm. What is its area?
First find the side: P = 4 × side → 40 = 4 × side, so side = 10 cm. Then area = 10 × 10 = 100 cm².
Q4.5 A square kitchen tile is 12 in on each side. What is its area?
A = 12 × 12 = 144 in². (That's 1 ft² — a standard floor tile.)
5. Composite shapes — split into rectangles
Poster 5 of 8 — Kid Einsteins Class 14
What if the shape isn't a rectangle?
Real rooms and yards are often L-shaped or T-shaped — not simple rectangles. The trick is to split them into rectangles you already know how to handle.
Steps for a composite area
Draw a dotted line to split the shape into 2 (or more) rectangles.
Label the sides of each rectangle. Sometimes you have to calculate a missing side by subtracting.
Find each rectangle's area using length × width.
Add the areas together.
For the L-shape on the poster:
Rectangle A (top): 4 × 3 = 12 m²
Rectangle B (bottom): 7 × 2 = 14 m²
Total: 12 + 14 = 26 m²
Perimeter of a composite shape
For perimeter, you still just add every outside side — but be careful not to include the dotted line you drew inside. The dotted line is only there to help you count area.
5 practice questions with hidden solutions
Q5.1 An L-shaped rug is made from a 5 ft × 4 ft rectangle on top and a 9 ft × 3 ft rectangle on the bottom. What is its total area?
The dashed line separates the two rectangles.
Q5.2 A patio is made of two rectangles: 6 m × 4 m and 3 m × 2 m. Find the total area.
The rectangles meet along an edge; they do not overlap.
6 × 4 = 24 m². 3 × 2 = 6 m². Total = 24 + 6 = 30 m².
Q5.3 A T-shaped hallway floor is a 10 ft × 3 ft rectangle across the top and a 4 ft × 6 ft rectangle hanging down from the middle. How many square feet of tile cover the floor?
The stem starts below the top rectangle.
Q5.4 An L-shape has outside sides of 8 cm, 4 cm, 4 cm, 6 cm, 4 cm, and 10 cm (going around). What is its perimeter?
Follow only the outside boundary.
Add every outside side. P = 8 + 4 + 4 + 6 + 4 + 10 = 36 cm. (The dotted line inside doesn't count.)
Q5.5 A garden is made of a big 10 m × 6 m rectangle with a small 2 m × 2 m rectangle cut OUT of one corner. What is the garden's area?
The dashed corner is cut out; only the shaded garden remains.
Big area minus small area. 10 × 6 = 60 m². 2 × 2 = 4 m². Garden = 60 − 4 = 56 m². (Cutting a piece out means subtracting.)
6. Finding a missing side
Poster 6 of 8 — Kid Einsteins Class 14
How do I find a side I'm not told?
Real problems often hide one of the sides. There are three everyday tricks.
Trick 1: use the shape's rule
In a rectangle, opposite sides are equal. So if the top is 9 cm, the bottom is also 9 cm. If the left is 4 cm, the right is also 4 cm.
In a square, all four sides are equal. So if you know one, you know all four.
Trick 2: work backwards from perimeter
If the problem tells you the perimeter and one side, use the formula in reverse.
If the problem tells you the area and one side, divide.
Example: area = 60 ft², length = 12 ft. Then width = 60 ÷ 12 = 5 ft. This uses Kid Einsteins Class 6 — division is the inverse of multiplication.
5 practice questions with hidden solutions
Q6.1 A rectangle has top = 15 cm. What is the bottom?
Opposite sides of a rectangle are equal. Bottom = 15 cm.
Q6.2 A rectangle has area 72 cm² and length 8 cm. What is the width?
Area = length × width → 72 = 8 × width. So width = 72 ÷ 8 = 9 cm.
Q6.3 A rectangle has perimeter 24 in and length 8 in. What is the width?
P = 2 × (length + width) → 24 = 2 × (8 + w). So 8 + w = 12, and w = 4 in.
Q6.4 A square has perimeter 32 cm. What is one side?
P = 4 × side → 32 = 4 × side. So side = 32 ÷ 4 = 8 cm.
Q6.5 A rectangle has area 48 ft² and width 6 ft. What is the length?
Area = length × width → 48 = length × 6. So length = 48 ÷ 6 = 8 ft.
7. Real-life word problems — fence vs paint
Poster 7 of 8 — Kid Einsteins Class 14
How do I turn a word problem into area vs perimeter?
Word problems rarely use the words "area" or "perimeter." You have to decide which one the problem is really asking for. Ask yourself: does the thing go AROUND the shape, or does it FILL the shape?
Around the shape → perimeter
Fence for a yard
Ribbon or lace or trim around a rectangle
Border around a poster or bulletin board
Baseboard or molding around a room
Walking around the outside of a track
Fills the shape → area
Paint for a wall
Carpet or rug or tile for a floor
Grass or sod for a yard
Wallpaper for a wall
Wrapping paper for a flat gift face
Poster example
Fence around a 20 ft × 15 ft yard: P = 20 + 15 + 20 + 15 = 70 ft of fence.
Paint for a 10 ft × 8 ft wall: A = 10 × 8 = 80 ft² of paint.
Notice how the units in your answer tell you which one you found: ft for a length (fence), ft² for a space (paint).
5 practice questions with hidden solutions
Q7.1 A rectangular yard is 30 ft by 20 ft. How much fence is needed to go around it?
Fence = perimeter = 30 + 20 + 30 + 20 = 100 ft.
Q7.2 A rectangular wall is 12 ft by 8 ft. How much paint (in ft²) is needed to cover it?
Paint = area = 12 × 8 = 96 ft².
Q7.3 A rectangular bulletin board is 4 ft by 3 ft. How much ribbon do you need to run around the edge?
Ribbon = perimeter = 4 + 3 + 4 + 3 = 14 ft.
Q7.4 A rectangular kitchen floor is 10 ft by 8 ft. How many square feet of tile cover the floor, and how many feet of baseboard run around it?
Q7.5 Grass costs $2 per square foot. How much does it cost to cover a rectangular yard that is 12 ft by 9 ft?
First find the area: A = 12 × 9 = 108 ft². Then cost = 108 × $2 = $216.
8. Same perimeter, different area
Poster 8 of 8 — Kid Einsteins Class 14
Do rectangles with the same perimeter have the same area?
Short answer: no. Two different rectangles can have the same perimeter and very different areas.
The poster's example
Rectangle A: 8 m × 2 m. P = 20 m. A = 16 m².
Rectangle B: 6 m × 4 m. P = 20 m. A = 24 m².
Same perimeter — but the more square-shaped rectangle holds more area. If you make the rectangle very long and skinny, it wastes area.
The big idea
For a fixed perimeter, the rectangle with the most area is the one closest to a square. This is why a square garden of 6 × 6 (P = 24, A = 36 cm²) beats every other rectangle with perimeter 24.
Where students go wrong
Many kids think "same perimeter means same area" or "same area means same perimeter." Both are false. Perimeter and area are different measurements. You have to compute each one separately.
5 practice questions with hidden solutions
Q8.1 Rectangle A is 6 × 4. Rectangle B is 8 × 2. Which one has more area? Which one has more perimeter?
A: area = 24, perimeter = 20. B: area = 16, perimeter = 20. A has more area; both have the same perimeter.
Q8.2 Find one rectangle with perimeter 16 cm that has a bigger area than a 6 × 2 rectangle (area 12 cm²).
Try 4 × 4: perimeter = 16 cm ✓, area = 16 cm². That's bigger than 12. (In fact, 4 × 4 gives the biggest area for perimeter 16.)
Q8.3 Rectangle A is 3 × 9. Rectangle B is 6 × 6. Both have perimeter 24. Which one has more area, and by how much?
A: area = 3 × 9 = 27 cm². B: area = 6 × 6 = 36 cm². Both perimeters check out (2 × (3 + 9) = 24 and 2 × (6 + 6) = 24). B has 9 cm² more area. The rectangle closest to a square wins.
Q8.4 A rectangle is 10 ft × 6 ft. Another is 12 ft × 4 ft. Compare their perimeters and areas.
First: P = 2 × (10 + 6) = 32 ft, A = 60 ft². Second: P = 2 × (12 + 4) = 32 ft, A = 48 ft². Same perimeter (32 ft); the first has more area.
Q8.5 True or false: if two rectangles have the same area, they must have the same perimeter.
False. Example: 4 × 6 and 3 × 8 both have area 24, but 4 × 6 has perimeter 20 and 3 × 8 has perimeter 22.
Homework review
Review the eight lesson topics with one question for each image, in the same order. Practice perimeter, area, units, squares, composite shapes, missing sides, and choosing the right measurement. Try each question before opening its answer.
R1. Image 1: A triangular flower bed has sides of 5 m, 6 m, and 7 m. What is its perimeter?Answer
18 m. Add every outside side once: 5 + 6 + 7 = 18. Perimeter uses length units, so the answer is meters.
R2. Image 2: A rectangle is 9 cm long and 5 cm wide. What is its area?Answer
45 cm². Area = length × width = 9 × 5 = 45. The rectangle contains 45 squares that each measure 1 cm by 1 cm.
R3. Image 3: A card is 7 cm long and 4 cm wide. Find its perimeter and area, and write the correct unit for each.Answer
Perimeter: 7 + 4 + 7 + 4 = 22 cm. Area: 7 × 4 = 28 cm². Use cm for the distance around and cm² for the space inside.
R4. Image 4: A square patio has sides of 8 m. Find its area and perimeter.Answer
Area: 8 × 8 = 64 m². Perimeter: 4 × 8 = 32 m. Squaring a side finds area; multiplying a side by four finds perimeter.
R5. Image 5: An L-shaped floor is split into two rectangles that do not overlap. One is 5 m by 3 m, and the other is 8 m by 2 m. What is the total area?Answer
31 m². The first rectangle has area 5 × 3 = 15 m². The second has area 8 × 2 = 16 m². Add the non-overlapping areas: 15 + 16 = 31 m².
R6. Image 6: A rectangular mat has an area of 42 ft² and a length of 7 ft. Find its width, then its perimeter.Answer
R7. Image 7: A rectangular garden is 9 m long and 4 m wide. How much fencing surrounds it, and what area needs grass?Answer
Fencing uses perimeter: 9 + 4 + 9 + 4 = 26 m. Grass covers area: 9 × 4 = 36 m². The two answers measure different things.
R8. Image 8: Garden A is 9 m by 3 m. Garden B is 7 m by 5 m. Compare their perimeters and areas. Which garden has more growing space, and by how much?Answer
Both perimeters are 24 m: 2 × (9 + 3) = 24 and 2 × (7 + 5) = 24. Garden A has area 27 m²; Garden B has area 35 m². Garden B provides 35 − 27 = 8 m² more growing space.
Homework word problems
Apply the class ideas to 12 word problems, moving from one-step questions to multi-step challenges. Together with the eight review questions, these make 20 homework questions.
W1. Mia puts ribbon around all four edges of an 8 cm by 3 cm photograph. How many centimeters of ribbon does she need?Answer
22 cm. Ribbon goes around the edge, so find the perimeter: 8 + 3 + 8 + 3 = 22 cm.
W2. A classroom reading corner is 7 ft long and 6 ft wide. How many square feet of carpet will cover it?Answer
42 ft². Carpet covers the inside, so find the area: 7 × 6 = 42 ft².
W3. A square sandbox has sides of 6 m. The school needs a border around it and a cover over the entire top. What border length and cover area are needed?Answer
Border: 4 × 6 = 24 m. Cover: 6 × 6 = 36 m². Use perimeter for the border and area for the cover.
W4. A rectangular vegetable bed has a perimeter of 24 m and a length of 8 m. What is its width, and how much planting area does it have?Answer
The two lengths use 8 + 8 = 16 m. The two widths use 24 − 16 = 8 m, so each width is 4 m. Planting area = 8 × 4 = 32 m².
W5. A rectangular art display covers 54 ft². It is 9 ft long. The teacher wants trim around all four sides. How many feet of trim are needed?Answer
First find the width: 54 ÷ 9 = 6 ft. Then find the perimeter: 9 + 6 + 9 + 6 = 30 ft of trim.
W6. An 11 m by 5 m dog run needs fencing, except for a 2 m opening for a gate. How many meters of fencing are needed?Answer
The complete perimeter is 2 × (11 + 5) = 32 m. Subtract the gate opening once: 32 − 2 = 30 m of fencing.
W7. A wall is 8 m wide and 4 m high. It has one window that is 2 m wide and 3 m high. What area of the wall needs paint if the window is not painted?Answer
Whole wall: 8 × 4 = 32 m². Window: 2 × 3 = 6 m². Painted area: 32 − 6 = 26 m².
W8. A library's L-shaped reading space consists of two non-overlapping rectangles: 6 m by 4 m and 3 m by 5 m. Each carpet tile covers 1 m². How many tiles cover the whole space?Answer
First rectangle: 6 × 4 = 24 m². Second rectangle: 3 × 5 = 15 m². Total area = 24 + 15 = 39 m². At 1 m² per tile, 39 tiles are needed.
W9. A rectangular play area is 12 m long and 7 m wide. A 4 m gate opening does not need fencing. Fencing costs $3 per meter. Find the fencing cost and the area inside the play area.Answer
Full perimeter: 2 × (12 + 7) = 38 m. Fence length: 38 − 4 = 34 m. Fence cost: 34 × $3 = $102. Interior area: 12 × 7 = 84 m².
W10. A square garden has sides of 10 m. A 4 m by 3 m corner is reserved for a patio. The rest is planted with four flowers per square meter. How many flowers are needed?Answer
Whole garden: 10 × 10 = 100 m². Patio: 4 × 3 = 12 m². Planting area: 100 − 12 = 88 m². Flowers: 88 × 4 = 352.
W11. A school has 28 m of fencing and no gate. It is choosing among gardens measuring 10 m by 4 m, 8 m by 6 m, or 7 m by 7 m. Check that each uses 28 m of fencing. Which has the most area, and how much more area does it have than the 10 m by 4 m garden?Answer
Perimeters: 2 × (10 + 4) = 28 m; 2 × (8 + 6) = 28 m; 4 × 7 = 28 m. Areas: 40 m², 48 m², and 49 m². The 7 m by 7 m square has the most area, providing 49 − 40 = 9 m² more than the first garden.
W12. A 12 m by 8 m yard contains a 3 m by 2 m shed. Grass covers the rest. An outside fence has a 2 m gate opening. Fencing costs $4 per meter and grass costs $2 per square meter. With a $350 budget, can the family pay for both? How much is left or missing?Answer
Kid Einsteins meets in person on the Upper West Side. Small groups of up to 6 students. Real teachers, not tutors or apps. Every family starts with a free in-person evaluation so we can place your child at the right point in the 48-class syllabus.
Perimeter is the distance around a shape — you add up every side, and the answer is in regular length units (cm, in, ft, m). Area is the space inside the shape — for a rectangle it's length × width, and the answer is in squared units (cm², in², ft², m²).
What is the formula for the area of a rectangle?
Area = length × width. If a rectangle is 6 cm long and 4 cm wide, its area is 6 × 4 = 24 cm². The answer is always in squared units.
What is the formula for the perimeter of a rectangle?
Perimeter = 2 × length + 2 × width, which is the same as 2 × (length + width). For an 8 cm × 5 cm rectangle: P = 2 × (8 + 5) = 26 cm.
How do I find the area of an L-shape or T-shape?
Split the shape into two rectangles with a dotted line. Find the area of each rectangle using length × width, then add the two areas together. For a rectangle with a corner cut out, find the big area and subtract the missing piece.
If two rectangles have the same perimeter, do they have the same area?
No. A 6 × 2 rectangle and a 4 × 4 square both have perimeter 16, but 6 × 2 has area 12 and 4 × 4 has area 16. For a fixed perimeter, the rectangle closest to a square holds the most area.
Which unit means area — cm or cm²?
cm² means area. The little 2 (called "squared") is the signal that two directions were multiplied together — length and width. Just cm (no little 2) means a length, so it's a perimeter or a single side.
What grade level is Kid Einsteins Class 14 for?
Grades 3–4 at SOMATH's Kid Einsteins course on the Upper West Side of NYC. Class 14 is part of the 48-class rolling syllabus and builds on multiplication (Classes 1–5) and division (Classes 6–7). The follow-up work in this topic continues in Class 32 (composite figures) and Class 33 (volume of rectangular prisms).
