Question

a frame shop charges according to both the amount of framing needed to surround the picture and the amount of glass needed to cover the picture. a. find the area and perimeter of the trapezoid - shaped framed picture to the right. b. identify whether the frame has to do with perimeter or area and the same with the glass. a. the area of the picture is 1188 sq in. and the perimeter is blank b. choose the correct answer below. a. both the frame and the glass have to do with area. b. the frame has to do with area and the glass has to do with perimeter. c. both the frame and the glass have to do with perimeter. d. the frame has to do with perimeter and the glass has to do with area.

Explanation:

Step1: Recall trapezoid area formula

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a = 18$ in, $b = 48$ in, and $h = 36$ in.
$A=\frac{(18 + 48)\times36}{2}=\frac{66\times36}{2}=66\times18 = 1188$ sq in.

Step2: Recall trapezoid perimeter formula

The perimeter $P$ of a trapezoid is the sum of the lengths of its four sides. $P=18 + 39+48 + 39=144$ in.
The glass is for covering the area (it fills the inside of the trapezoid - shaped picture), and the frame is for going around the outside (perimeter).

Answer:

a. 144 in
b. A. Both the frame and the glass have to do with area.