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
480 square units
480 square units
864 square units
864 square units
288 square units
288 square units
576 square units
The correct answer is:
576 square units
To find the area of the frame, you need to find the area of the outer rectangle and the area of the inner rectangle, then subtract the area of the inner rectangle from the area of the outer rectangle.
Area of outer rectangle = length * width = 36 * 24 = 864 square units
Area of inner rectangle = (length - 2*4) * (width - 2*6) = 28 * 12 = 336 square units
Area of frame = Area of outer rectangle - Area of inner rectangle = 864 - 336 = 528 square units