Use 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, we need to find the area of each of the shapes and then add them up.
1. Rectangle on the left:
Area = length x width = 4 cm x 3 cm = 12 cm²
2. Square in the middle:
Area = side x side = 3 cm x 3 cm = 9 cm²
3. Rectangle on the right:
Area = length x width = 5 cm x 3 cm = 15 cm²
4. Two right triangles:
Area = 1/2 x base x height = 1/2 x 3 cm x 4 cm = 6 cm² (for each triangle, so a total of 12 cm²)
Now, add up the areas of all the shapes:
12 cm² + 9 cm² + 15 cm² + 12 cm² = 48 cm²
Therefore, the surface area of the shown net for a triangular prism is 48 cm².