Use Area to Solve Problems Quick Check
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Question
Use the image to answer the question.
An illustration shows two concentric rectangles, an outer and an inner rectangle. The length of the outer rectangle shown vertically is labeled as 36. The width labeled horizontally is 24. The distance between the lengths of the outer and inner rectangle is labeled as 4 on the left and right. The distance between the widths of the outer and inner rectangle is labeled as 6 on the top and bottom. The distances are shown using dashed lines.
A picture framer is painting the front of a picture frame. What is the area of the frame? Assume that all segments that look congruent are congruent and all angles that look like right angles are right angles.
(1 point)
Responses
288
288
480
480
576
576
864
what is the EXACT answer? also provide a step by step explanation.
The area of the frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle.
The outer rectangle has a length of 36 and a width of 24, so its area is:
36 x 24 = 864
The inner rectangle has a length of 36 - 2(4) = 28 and a width of 24 - 2(6) = 12, so its area is:
28 x 12 = 336
Therefore, the area of the frame is:
864 - 336 = 528
The exact answer is 528.