Use the image to answer the question.

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

Answer 1

To find the surface area of the triangular prism, we first need to find the area of each individual face on the net.

1. The area of the front and back rectangles:
3cm (width) x 4cm (length) = 12cm² for each rectangle
Total for both rectangles = 2 x 12cm² = 24cm²

2. The area of the middle square:
3cm x 3cm = 9cm²

3. The area of the two right triangles:
(1/2) x 4cm x 3cm = 6cm² for each triangle
Total for both triangles = 2 x 6cm² = 12cm²

Now, add together the areas of all the faces:
24cm² (rectangles) + 9cm² (square) + 12cm² (triangles) = 45cm²

Therefore, the total surface area of the triangular prism shown in the net is 45 cm².