Question

how many square feet of drywall are needed for the wall shown in the figure to the right?

Answer 1

Answer:

174.5 square feet of drywall are needed

Step-by-step explanation:

The picture of the question in the attached figure

we know that

we can divide the figure into a trapezoid and a rectangle (the door)

so

To find out how many square feet of drywall are needed, subtract the area of the rectangle minus the area of trapezoid

step 1

Find the area of trapezoid

The area of trapezoid is equal to

$A_1=\frac{1}{2}[b_1+b_2]h$

where

b_1 and b_2 are the parallel bases

h is the height (perpendicular distance between the parallel bases)

substitute the given values

$A_1=\frac{1}{2}[9+14]17=195.5\ ft^2$

step 2

Find the area of the rectangular door

we know that

The area of rectangle is

$A_2=bh$

where

b is the base of the door

h is the height of the door

substitute the given values

$A_2=(3)(7)=21\ ft^2$

step 3

Subtract the areas

$195.5\ ft^2-21\ ft^2=174.5\ ft^2$

therefore

174.5 square feet of drywall are needed