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
253.6 cm2
253.6 cm squared
174.8 cm2
174.8 cm squared
120 cm2
120 cm squared
126.8 cm2
126.8 cm squared
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To calculate the lateral surface area of the triangular prism represented by the net diagram, we first need to find the lateral surface area of each triangular face and then add them together.
For the center triangle:
Base = 12 cm
Height = 8 cm
Lateral surface area = 1/2 * base * height
= 1/2 * 12 cm * 8 cm
= 48 cm²
For the three connected triangles:
Triangle 1:
Base = 12 cm
Height = 7.8 cm
Lateral surface area = 1/2 * base * height
= 1/2 * 12 cm * 7.8 cm
= 46.8 cm²
Triangle 2 & 3:
Base = 10 cm
Height = 8 cm
Lateral surface area = 1/2 * base * height
= 1/2 * 10 cm * 8 cm
= 40 cm² each
Total lateral surface area = 48 cm² + 46.8 cm² + 40 cm² + 40 cm²
= 174.8 cm²
Therefore, the correct answer is:
174.8 cm²