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 $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a = 27$ in, $b = 51$ in, and $h = 16$ in.
$A=\frac{(27 + 51)\times16}{2}=\frac{78\times16}{2}=78\times8 = 624$ square inches.

Step2: Calculate the perimeter of the trapezoid

The perimeter $P$ of a trapezoid is the sum of the lengths of its four sides. $P=27 + 20+51 + 20=118$ inches.

Answer:

The area of the picture is 624 square inches and the perimeter is 118 inches.