Mariko has a bedroom wall that is shaped like a trapezoid with a height of 8 ft, a top base of 10 ft, and a bottom base of 13 ft. In the middle of this wall is a circular window whose radius is 2 ft. What is the area of the wall without the window? Use 3.14 for pi.

Question

Mathematics

Nico Huerta

10 January, 03:57

Mariko has a bedroom wall that is shaped like a trapezoid with a height of 8 ft, a top base of 10 ft, and a bottom base of 13 ft. In the middle of this wall is a circular window whose radius is 2 ft. What is the area of the wall without the window? Use 3.14 for pi.

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Rayan Mcfarland · Answer 1

First, you have to find the area of the entire wall, including the window. The formula for the area of a trapezoid is:

A = (b1 + b2) / 2 * h

b1 is the first base, b2 is the second base, A is the total area, and h is the height.

Plug in the numbers from the problem.

(13 + 10) / 2 * 8

Simplify.

(23) / 2*8

11.5*8 = 92

Now, to calculate the window's surface area, you use the formula for area of a circle.

A = 3.14*r^2

Plug in your number.

A = 3.14 * 2^2

Simplify.

A = 3.14 * 4

A = 12.56

Now, you subtract the area of the window from the total area of the wall.

92 - 12.56 = 79.44

79.44 feet