Perimeter of Compound Shapes

Question 1

Jake is designing a play‑area floor by joining two rectangles so that they share one whole side. The first rectangle measures 8 cm by 5 cm. Which set of dimensions for the second rectangle will give the combined shape a perimeter of exactly 40 cm?

Accepted Answer

8 cm × 7 cm

Answer

5 cm × 6 cm

Answer

8 cm × 4 cm

Answer

5 cm × 9 cm

Question 2

Maya wants to draw a shape made by joining two rectangles so that they share one complete side. Which pair of rectangle dimensions will give her drawing a perimeter of exactly 40 cm?

Accepted Answer

One rectangle 10 cm by 3 cm joined to a rectangle 10 cm by 7 cm along the 10‑cm side.

Answer

One rectangle 9 cm by 4 cm joined to a rectangle 9 cm by 6 cm along the 9‑cm side.

Answer

One rectangle 8 cm by 5 cm joined to a rectangle 8 cm by 8 cm along the 8‑cm side.

Answer

One rectangle 12 cm by 2 cm joined to a rectangle 12 cm by 4 cm along the 12‑cm side.

Question 3

Sam wants to make a garden plot that is made by joining two rectangles edge‑to‑edge. Which of the following descriptions would give the whole plot a perimeter of exactly 40 cm?

Accepted Answer

A 10 cm × 6 cm rectangle with a 4 cm × 6 cm rectangle attached along the 6‑cm side.

Answer

A 9 cm × 7 cm rectangle with a 5 cm × 7 cm rectangle attached along the 7‑cm side.

Answer

An L‑shaped plot formed by cutting a 3 cm × 3 cm corner out of a 12 cm × 9 cm rectangle.

Answer

Two 5 cm × 5 cm squares placed side by side sharing one side.

Try three questions

Jake is designing a play‑area floor by joining two rectangles so that they share one whole side. The first rectangle measures 8 cm by 5 cm. Which set of dimensions for the second rectangle will give the combined shape a perimeter of exactly 40 cm?

Maya wants to draw a shape made by joining two rectangles so that they share one complete side. Which pair of rectangle dimensions will give her drawing a perimeter of exactly 40 cm?

Sam wants to make a garden plot that is made by joining two rectangles edge‑to‑edge. Which of the following descriptions would give the whole plot a perimeter of exactly 40 cm?

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