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 □

Explanation:

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), where \(b_1 = 20\) in, \(b_2=38\) in, and \(h = 12\) in.

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Step2: Calculate the perimeter of the trapezoid

The perimeter \(P\) of a trapezoid is the sum of all its sides. \(P=20 + 15+38 + 15\)

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Step3: Determine the relation of frame and glass

The frame is around the picture, so it is related to the perimeter. The glass covers the picture, so it is related to the area.

Answer:

a. The area of the picture is \(348\) square inches and the perimeter is \(88\) inches.
b. The frame has to do with perimeter and the glass has to do with area.