se the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as a rectangle, a square, and another rectangle joined horizontally next to each other. The width of the two rectangles and the side of the square measure 3 centimeters. The length of the left rectangle is 4 centimeters. The side of the middle square, drawn in a dashed line, is 3 centimeters. The length of the right rectangle is 5 centimeters. Two right triangles adjoin the middle square at the top and bottom, with each perpendicular side measuring 4 centimeters and each hypotenuse measuring 5 centimeters.
What is the surface area of the shown net for a triangular prism?
(1 point)
cm2
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To find the surface area of the net for a triangular prism, we need to calculate the area of each of the individual shapes and then add them together.
The rectangle on the left has a length of 4 cm and a width of 3 cm, so its area is 4 cm * 3 cm = 12 cm^2.
The square in the middle has a side length of 3 cm, so its area is 3 cm * 3 cm = 9 cm^2.
The rectangle on the right has a length of 5 cm and a width of 3 cm, so its area is 5 cm * 3 cm = 15 cm^2.
There are also two right triangles, each with a base of 3 cm and height of 4 cm. The area of one right triangle is 1/2 * base * height = 1/2 * 3 cm * 4 cm = 6 cm^2. Since there are two right triangles, their combined area is 2 * 6 cm^2 = 12 cm^2.
Adding up the areas of all the shapes, we get:
12 cm^2 (left rectangle) + 9 cm^2 (middle square) + 15 cm^2 (right rectangle) + 12 cm^2 (right triangles) = 48 cm^2.
Therefore, the surface area of the shown net for a triangular prism is 48 cm^2.