MATH SOLVE

2 months ago

Q:
# HELP. TODD.Kristine has a bedroom wall that is shaped like a trapezoid with a height of 9 ft, a top base of 12 ft, and a bottom base of 15 ft. In the middle of this wall is a circular window whose radius is 3 ft.What is the area of the wall without the window?Use 3.14 for pi.Enter your answer in the box.

Accepted Solution

A:

First, we figure out the area of the wall, which is shaped like a trapezoid. The equation for the area of a trapezoid is

[tex] \frac{1}{2} (a+b)h[/tex]

where a is the top base, b is the bottom base and h is the height.

Substitute your given values into the equation and solve:

A=1/2(12+15)9

A=4.5(27)

Area of the wall= 121.5ft²

Now we figure out the area of the of the circular window. The formula for the area of a circle is

[tex] \pi r^{2} [/tex]

where r is the radius

Substitute your given values into the equation and solve:

pi×3²

[tex]9 \pi =28.27433388 ft^{2} [/tex]

Now finally minus the area of the window from the area of the wall.

121.5-28.27433388=93.22566612

To 1 d.p., the area of the wall without the window is 93.2ft²

[tex] \frac{1}{2} (a+b)h[/tex]

where a is the top base, b is the bottom base and h is the height.

Substitute your given values into the equation and solve:

A=1/2(12+15)9

A=4.5(27)

Area of the wall= 121.5ft²

Now we figure out the area of the of the circular window. The formula for the area of a circle is

[tex] \pi r^{2} [/tex]

where r is the radius

Substitute your given values into the equation and solve:

pi×3²

[tex]9 \pi =28.27433388 ft^{2} [/tex]

Now finally minus the area of the window from the area of the wall.

121.5-28.27433388=93.22566612

To 1 d.p., the area of the wall without the window is 93.2ft²