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
864 square units
864 square units
480 square units
480 square units
576 square units
576 square units
288 square units
288 square units
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To find the area of the frame, we first need to find the area of the outer rectangle and the area of the inner rectangle.
The area of the outer rectangle is 36 * 24 = 864 square units.
The area of the inner rectangle can be calculated by subtracting the area of the inner rectangle from the area of the outer rectangle.
The length of the inner rectangle is 36 - 2*4 = 28, and the width of the inner rectangle is 24 - 2*6 = 12.
So, the area of the inner rectangle is 28 * 12 = 336 square units.
Therefore, the area of the frame is 864 - 336 = 528 square units.
Therefore, the correct answer is not listed, but closest is 576 square units.