Question

in this section, youll solve problems involving surface area, perimeter, and volume. youre now going to experiment with streaming content from home. you plan to cover a panel with an attractive fabric for use as a backdrop, and you need to determine how much fabric to buy. whats the area of this shape? 18 ft.² 30 ft.² 24 ft.² 36 ft.²

Explanation:

Step1: Calculate the length of the other base

The figure is a trapezoid. The formula for the area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\). We know one base \(b_1 = 9\) ft, the height \(h=4\) ft. To find the other base \(b_2\), we use the fact that in the right - triangle part (formed by the height, the difference between the bases, and the non - parallel side), if the non - parallel side (slant side) is \(5\) ft and the height is \(4\) ft, by the Pythagorean theorem \(a=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}=3\) ft. Then \(b_2=9-(3 + 3)=3\) ft.

Step2: Calculate the area of the trapezoid

Substitute \(b_1 = 9\) ft, \(b_2 = 3\) ft, and \(h = 4\) ft into the area formula \(A=\frac{(b_1 + b_2)h}{2}\).

$$
LATEXBLOCK0
$$

Answer:

\(24\space ft^{2}\)