An illustration shows a net diagram. The center of the diagram is a triangle. Each side of the center triangle forms the base of one of three triangles extending outward from the center triangle. The center triangular base has a base edge measuring 12 centimeters, two side edges measuring 10 centimeters, and a perpendicular height measuring 8 centimeters. Its sides are marked by dashed lines, which form the bases of three connected triangles. One of the connected triangles has a base measuring 12 centimeters and a perpendicular height of 7.8 centimeters. The other two connected triangles have bases measuring 10 centimeters and perpendicular heights measuring 8 centimeters. Which of the following is the lateral surface area of the triangular prism represented with a net?
To find the lateral surface area of the triangular prism represented by the net diagram, we need to calculate the lateral surface area of each of the four triangles and then add them up.
Lateral surface area of the center triangle:
Lateral surface area = (perimeter of base * height) / 2
= ((10 + 10 + 12) * 8) / 2
= (32 * 8) / 2
= 256 / 2
= 128 square centimeters
Lateral surface area of the triangle with base 12 cm and height 7.8 cm:
Lateral surface area = 12 * 7.8
= 93.6 square centimeters
Lateral surface area of the two triangles with base 10 cm and height 8 cm:
Lateral surface area for each triangle = 10 * 8 / 2
= 40 square centimeters
Total for both triangles = 40 + 40 = 80 square centimeters
Therefore, the total lateral surface area of the triangular prism represented by the net diagram is:
128 + 93.6 + 80 = 301.6 square centimeters
So, the lateral surface area of the triangular prism represented with the net is 301.6 square centimeters.