What is the perimeter of the figure shown?

Step 1: To find the perimeter of a figure, you can add the length of each side. The length of each side is not shown, but can be found.

One section is missing. The full height of the square area is 10 feet. The triangular area is 5 feet high.

10 ft – 5 ft = 5 ft

Step 2: Add the length of each side. Choose a side to begin, and add in order around the figure.

10 ft + 10 ft + 20 ft + 11 ft + 5 ft = 56 ft

The perimeter of the figure is 56 feet.

TEST TIME: Show Your Work

Harrison needs to carpet his closet. The closet is rectangular, but has a raised triangular area that does not need carpet. Using the diagram, how many square feet of carpet does Harrison need?

Areas that are made up of polygons like rectangles and triangles can be found by adding or subtracting theareas of the polygons they are made of.

Solution: Find the area of each figure.
Area of the rectangle = lw
= (8)(9)
= 72

Area of the triangle = ¹/₂bh
= ¹/₂(4)(4)
= 8

Subtract the area of the triangle from the area of the rectangle.

72 square feet ‒ 8 square feet = 64 square feet

Harrison needs 64 square feet of carpet.

Test-Taking Hint

Most tests are scored on the number of questions you answer correctly. You do not lose points for wrong answers. Answer every question, even if you have to guess.

Using Area

The area outlined in red is a garden plot. The green-shaded area produced 3 quarts of green beans. If the entire garden is planted in green beans, about how many quarts of beans can be produced?

Step 1: Estimate the area inside the red outline.

Whole or nearly whole units: 19
Half or near half units: 8

Whole units + half of partial units: 19 + 4 = 23

Step 2: Each of the units that are planted in beans will produce about 3 quarts of beans. Multiply the number of units by 3 quarts.

23 × 3 quarts = 69 quarts

The entire garden can produce around 69 quarts of beans.

20

Combined Figures