Kid Einsteins Class 14: Area, Perimeter & Word Problems — 8 SOMATH Posters, Theory & 40 Practice Questions

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.

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.

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:

• Perimeter (distance around): fence, ribbon, border, trim, molding, wire, walking track.
• Area (space inside): paint, carpet, grass, tile, wallpaper, wrapping paper, floor covering.

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."

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

1. Draw a dotted line to split the shape into 2 (or more) rectangles.
2. Label the sides of each rectangle. Sometimes you have to calculate a missing side by subtracting.
3. Find each rectangle's area using length × width.
4. Add the areas together.

For the L-shape on the poster:

• Rectangle A (top): 4 × 4 = 16 cm²
• Rectangle B (bottom): 10 × 4 = 40 cm²
• Total: 16 + 40 = 56 cm²

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.

How do I find a side I'm not told?

Real problems often hide one of the sides. There are two 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.

Example: perimeter = 30 cm, length = 10 cm.

P = 2 × length + 2 × width

30 = 2 × 10 + 2 × width → 30 = 20 + 2w → 2w = 10 → w = 5 cm

Trick 3: work backwards from area

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.

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).

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 1: 8 cm × 4 cm. P = 24 cm. A = 32 cm².
• Rectangle 2: 10 cm × 2 cm. P = 24 cm. A = 20 cm².

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.