Use the image to answer the question.
An illustration shows two rectangles intersecting, one is oriented horizontally and the other is oriented vertically. Their dimensions are labeled are they are divided into segments. The dimensions of the horizontal rectangle are as follows: It is divided into four segments. The first segment is labeled 3 inches horizontal and 8 inches vertical. The second segment is labeled 6 inches horizontal. The third segment is the intersection common area and is not labeled. The fourth segment is 6 inches horizontal and 8 inches vertical. The dimensions of the vertical rectangle are as follows: It is divided into three segments. The top segment is labeled 3 inches horizontal and 6 inches vertical. The second segment is the intersection common area and is not labeled. The third segment is labeled 6 inches vertical.
A necklace comes in a jewelry box whose net is shown in this image. What is the surface area of the box?
(1 point)
in.2
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To find the surface area of the box, we need to calculate the total area of all the individual rectangles that make up the net of the box.
The horizontal rectangle:
- First segment: 3 inches x 8 inches = 24 square inches
- Second segment: 6 inches x 6 inches = 36 square inches
- Fourth segment: 6 inches x 8 inches = 48 square inches
Total area of the horizontal rectangle = 24 + 36 + 48 = 108 square inches
The vertical rectangle:
- Top segment: 3 inches x 6 inches = 18 square inches
- Third segment: 6 inches x 6 inches = 36 square inches
Total area of the vertical rectangle = 18 + 36 = 54 square inches
Adding the total areas of the horizontal and vertical rectangle together, we get:
Total surface area of the jewelry box = 108 + 54 = 162 square inches
Therefore, the surface area of the box is 162 in^2.