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?
576
how do you know?
To find the area of the frame, we need to subtract 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 is formed by shifting its sides 4 units inwards from the sides of the outer rectangle. Therefore, it has a length of 36 - 2(4) = 28 and a width of 24 - 2(6) = 12. So its area is 28 x 12 = 336.
To find the area of the frame, we subtract the area of the inner rectangle from the area of the outer rectangle:
864 - 336 = 528
So the area of the frame is 528. However, the options only give an approximation, and the closest one to the actual value is 576.
To find the area of the frame, we need to calculate the area of the outer rectangle and subtract the area of the inner rectangle.
The length of the outer rectangle is given as 36, and the width is given as 24. Therefore, the area of the outer rectangle can be calculated by multiplying the length by the width: 36 * 24 = 864.
Now, let's find the area of the inner rectangle. The length and width of the inner rectangle can be found by subtracting the distances between the lengths and widths of the outer and inner rectangles from the dimensions of the outer rectangle.
The length of the inner rectangle is calculated as: 36 - 2*4 = 36 - 8 = 28.
The width of the inner rectangle is calculated as: 24 - 2*6 = 24 - 12 = 12.
Therefore, the area of the inner rectangle is: 28 * 12 = 336.
To find the area of the frame, we subtract the area of the inner rectangle from the area of the outer rectangle: 864 - 336 = 528.
So, the exact answer for the area of the frame is 528 square units.