Question

how many square feet of outdoor carpet will we need for this hole? 2 ft, 3 ft, 6 ft, 3 ft, 11 ft

Explanation:

Step1: Find the area of the rectangle

The formula for the area of a rectangle is \( A = length \times width \). The length of the rectangle is 11 ft and the width is 6 ft. So, \( A_{rectangle} = 11 \times 6 = 66 \) square feet.

Step2: Find the base of the triangle

The base of the triangle can be found by subtracting the sum of the two given segments from the length of the rectangle. The sum of the two segments is \( 2 + 3 = 5 \) ft. So, the base of the triangle \( b = 11 - 5 = 6 \) ft.

Step3: Find the height of the triangle

The height of the triangle is the difference between the height of the rectangle and the given vertical segment. So, \( h = 6 - 3 = 3 \) ft.

Step4: Find the area of the triangle

The formula for the area of a triangle is \( A = \frac{1}{2} \times base \times height \). Substituting the values, we get \( A_{triangle} = \frac{1}{2} \times 6 \times 3 = 9 \) square feet.

Step5: Find the area of the carpet (green area)

The area of the carpet is the area of the rectangle minus the area of the triangle. So, \( A = A_{rectangle} - A_{triangle} = 66 - 9 = 57 \) square feet.

Answer:

57