Area, perimeter, and estimating shapes

Mathematics · Measurement · ages 9-10

Name ______________________ Date ____________

A square has sides of 4 cm. What is its area, in cm²?
Answer: ______________
A rectangle is 5 cm long and 3 cm wide. What is its area?
- 8 cm²
- 15 cm²
- 16 cm²
True or false: the perimeter of a rectangle is the same as adding up the length of all four sides.
Circle one: True False
A square tile has sides of 7.5 cm. What is its area, in cm²?
Answer: ______________
A room has an area of 48 m² and a length of 8 m. What is its width, in metres?
Answer: ______________
A garden is 10 m long and 4 m wide. What is its perimeter?
- 14 m
- 28 m
- 40 m
A pond is drawn on a cm² grid. It covers 14 whole squares completely, plus 6 more squares that are about half-covered. What is the best estimate of its area?
- 14 cm²
- 17 cm²
- 20 cm²
Ben says a rectangle that is 9 cm by 6 cm has an area of 30 cm², because he added 9 + 9 + 6 + 6. What did Ben actually calculate?
- The perimeter, not the area
- The area, correctly
- Half of the area

Answer key

For grown-ups. Fold this page away before handing over the rest.

16 · A square's area is side × side: 4 × 4 = 16 cm².
15 cm² · Area of a rectangle is length × width: 5 × 3 = 15 cm². Adding the sides only works for perimeter.
True · Perimeter is the total distance around a shape, so adding all four sides always works. The shortcut 2 × length + 2 × width just makes it faster because opposite sides match.
56.25 · Area = side × side = 7.5 × 7.5 = 56.25 cm².
6 · Since area = length × width, width = area ÷ length = 48 ÷ 8 = 6 m.
28 m · Perimeter = 2 × length + 2 × width = 2 × 10 + 2 × 4 = 28 m.
17 cm² · Count the whole squares first (14), then add your best guess for the part squares. Six half-squares add about 3 more, giving 17 cm².
The perimeter, not the area · Adding all the sides gives the perimeter (30 cm), not the area. The area needs multiplication: 9 × 6 = 54 cm².