Walk around the border

The idea

The perimeter of a shape is the total length around its border: 4a for a square of side a, 3a for an equilateral triangle of side a, and 2(a + b) for a rectangle with sides a and b.

An insect on a walk

A tiny insect goes for a walk around the border of a shape. It never turns around, and it stops when it is back at its starting point.

The shape is a square with side a. How far does the insect walk in one round?

• a
• 2a
• 4a

Round the border

Tap Next side to move the insect one side at a time. Watch the sides add up.

The total distance

The perimeter of a shape is the total length around its border. A square of side a has perimeter 4a. An equilateral triangle of side a has perimeter 3a. A rectangle with sides a and b has perimeter 2(a + b).

The perimeter is the total distance the insect travels. In a rectangle the sides come in pairs, so a + b + a + b = 2(a + b).

Notes

The perimeter is the total length around the border: 4a for a square, 3a for an equilateral triangle, 2(a + b) for a rectangle.

Check yourself

A square plot has side 12 m. What is its perimeter?

Answer: 48 m

4 × 12 = 48 m.

An equilateral triangle has side 9 cm. What is its perimeter?

A rectangle is 8 cm long and 5 cm wide. What is its perimeter?

Answer: 26 cm

2(8 + 5) = 2 × 13 = 26 cm.

A rectangle has sides a and b. Which expression gives its perimeter?

• 27 cm — correct. Yes. Three equal sides: 3 × 9 = 27.
• 18 cm. That is only two sides. The insect also walks the third.
• 81 cm. 9 × 9 is not a length around the border. The perimeter is 3 × 9.
• a + b. That is only two of the four sides.
• 2(a + b) — correct. Yes. Two sides of length a and two of length b.
• ab. ab is the area of the rectangle, not its perimeter.