Find the area and perimeter of each composite shape.

Steps to Solve

1. Calculate the area of Shape 4

Shape 4 is a composite shape made up of a rectangle and a square. Divide the shape into a rectangle and a square. The area of the rectangle is $length \times width = 6 \times 7 = 42 \text{ yd}^2$. The area of the square is $side \times side = 3 \times 3 = 9 \text{ yd}^2$. Since there are two squares, the total area of the squares is $2 \times 9 = 18 \text{ yd}^2$. Add the area of the rectangle to the total area of the squares, $42 + 18 = 60 \text{ yd}^2$.

2. Calculate the perimeter of Shape 4

The perimeter is the sum of all the sides. The sides are 7, 6, 7, 3, 3, 3, 3. The perimeter is $7 + 6 + 7 + 3 + 3 + 3 + 3 = 32 \text{ yd}$.

3. Calculate the area of Shape 5

Shape 5 is made of two rectangles. The area of the big rectangle is $12 \times 12 = 144 \text{ ft}^2$. The area of the small rectangle is $4 \times 4 = 16 \text{ ft}^2$. Thus the total area is $144 + 16 = 160 \text{ ft}^2$.

4. Calculate the perimeter of Shape 5

Looking at Shape 5, the perimeter is all the sides added together. The sides are 12, 12, 4, 4, 4, 4, 8, 8. $P = 12 + 12 + 4 + 4 + 4 + 4 + 8 + 8 = 56 \text{ ft}$.