Use the image to answer the question.
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?
(1 point)
Responses
120 cm2
120 cm squared
126.8 cm2
126.8 cm squared
174.8 cm2
174.8 cm squared
253.6 cm2
253.6 cm squared
Skip to navigation
To find the lateral surface area of the triangular prism represented by the net diagram, we need to calculate the sum of the lateral surface areas of the three connected triangles.
For the center triangle:
Lateral surface area = sum of the areas of two sides
= 2 * 10 cm * 8 cm = 160 cm^2
For the triangle with base 12 cm and height 7.8 cm:
Lateral surface area = base perimeter * height / 2
= 12 cm * 7.8 cm / 2 = 46.8 cm^2
For the triangles with base 10 cm and height 8 cm:
Lateral surface area = base perimeter * height / 2
= 10 cm * 8 cm / 2 = 40 cm^2 each
Therefore, the total lateral surface area is:
160 cm^2 + 46.8 cm^2 + 40 cm^2 + 40 cm^2 = 286.8 cm^2
So the correct answer is: 286.8 cm2.