Perimeter (age 10+)

Question 1

Two shapes each have an area of 36 cm². Shape A is a square, and Shape B is a long, thin rectangle. Which statement best explains why Shape B’s perimeter is larger than Shape A’s?

Accepted Answer

Because the rectangle’s length and width are more unequal, the sum of its four sides (the perimeter) is greater even though the product of the sides (the area) is the same.

Answer

Because a square always has the same perimeter as any rectangle with the same area.

Answer

Because the rectangle has more corners than the square.

Answer

Because the rectangle’s sides are measured in centimeters while the square’s sides are measured in meters.

Question 2

Which pair of shapes both have a perimeter of exactly 20 cm but have different areas?

Accepted Answer

A rectangle 3 cm × 7 cm and a square 5 cm × 5 cm

Answer

A rectangle 2 cm × 8 cm and a rectangle 4 cm × 5 cm

Answer

Two squares each 5 cm × 5 cm

Answer

A rectangle 1 cm × 9 cm and a rectangle 2 cm × 9 cm

Question 3

A class is making two garden beds that each must have a perimeter of exactly 18 cm. Which pair of rectangular beds meets this requirement and also has different areas?

Accepted Answer

A 2 cm × 7 cm rectangle and a 4 cm × 5 cm rectangle.

Answer

A 3 cm × 6 cm rectangle and another 3 cm × 6 cm rectangle.

Answer

A 4 cm × 5 cm rectangle and a 5 cm × 5 cm square.

Answer

A 1 cm × 8 cm rectangle and a 2 cm × 9 cm rectangle.

Try three questions

Two shapes each have an area of 36 cm². Shape A is a square, and Shape B is a long, thin rectangle. Which statement best explains why Shape B’s perimeter is larger than Shape A’s?

Which pair of shapes both have a perimeter of exactly 20 cm but have different areas?

A class is making two garden beds that each must have a perimeter of exactly 18 cm. Which pair of rectangular beds meets this requirement and also has different areas?

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