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 and the perimeter is 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 and perimeter formulas

Area of trapezoid $A=\frac{(a + b)h}{2}$, perimeter $P=a + b + c + d$ (where $a,b$ are parallel - sides and $c,d$ are non - parallel sides, $h$ is height).
For the trapezoid with parallel sides $a = 18$ in and $b = 48$ in, and height $h = 36$ in.
$A=\frac{(18 + 48)\times36}{2}=\frac{66\times36}{2}=66\times18 = 1188$ square inches.
To find the perimeter, we need to know the lengths of the non - parallel sides. Assuming we have all side lengths, we sum them up.
The glass covers the area of the picture (trapezoid), and the frame goes around the perimeter of the picture.

Step2: Analyze the relationship between frame and glass

The glass is for covering the inner part (area) of the picture, and the frame is for going around the outer edge (perimeter) of the picture.
The frame has to do with perimeter and the glass has to do with area.

Answer:

a. Area of the picture: 1188 square inches (assuming the trapezoid area formula application as above).
b. A. Both the frame and the glass have to do with area. (This is incorrect as the frame is related to perimeter and the glass is related to area). The correct answer for part b should be that the frame has to do with perimeter and the glass has to do with area. So, the answer for part b is not among the given options as presented, but the correct concept is that the frame is about perimeter and the glass is about area.