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
864
To find the area of the frame, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
First, let's find the area of the outer rectangle. We can use the formula for the area of a rectangle: A = length * width. From the information given, we know that the length of the outer rectangle is 36 and the width is 24.
Area of outer rectangle = 36 * 24 = 864.
Next, let's find the area of the inner rectangle. To do this, we need to subtract the areas of the four corners from the area of the outer rectangle.
The two corners on the left and right sides have a distance of 4 between the lengths of the outer and inner rectangles. Therefore, the width of each corner is 4.
The two corners on the top and bottom sides have a distance of 6 between the widths of the outer and inner rectangles. Therefore, the length of each corner is 6.
Now, we can find the area of each corner rectangle:
Area of left corner = 4 * 6 = 24.
Area of right corner = 4 * 6 = 24.
Area of top corner = 6 * 4 = 24.
Area of bottom corner = 6 * 4 = 24.
Since there are four corner rectangles, we need to multiply the area of one corner by 4 to get the total area of all four corners.
Total area of corners = (24 + 24 + 24 + 24) * 4 = 96 * 4 = 384.
Finally, we can find the area of the inner rectangle by subtracting the total area of the corners from the area of the outer rectangle.
Area of inner rectangle = Area of outer rectangle - Total area of corners = 864 - 384 = 480.
So, the area of the frame is 480.
The area of the frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle. The length of the inner rectangle can be found by subtracting the total distance between the lengths (4+4=8) from the length of the outer rectangle (36-8=28). Similarly, the width of the inner rectangle can be found by subtracting the total distance between the widths (6+6=12) from the width of the outer rectangle (24-12=12). Thus, the area of the frame is:
(36 x 24) - (28 x 12) = 864
Therefore, the answer is 864.
To find the area of the frame, we need to calculate the difference between the area of the outer rectangle and the area of the inner rectangle.
The length of the outer rectangle is 36, and the width is 24. Therefore, the area of the outer rectangle is 36 x 24 = 864.
The distance between the lengths of the outer and inner rectangle is 4 on each side, and the distance between the widths of the outer and inner rectangle is 6 on each side.
To find the dimensions of the inner rectangle, subtract twice the distance (4 + 4) from the length and width of the outer rectangle:
Length of inner rectangle = 36 - 2(4) = 36 - 8 = 28
Width of inner rectangle = 24 - 2(6) = 24 - 12 = 12
The area of the inner rectangle is 28 x 12 = 336.
Finally, subtract the area of the inner rectangle from the area of the outer rectangle to find the area of the frame:
Area of frame = Area of outer rectangle - Area of inner rectangle = 864 - 336 = 528.
Therefore, the area of the frame is 528.