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
126.8 cm2
126.8 cm squared
120 cm2
120 cm squared
174.8 cm2
174.8 cm squared
253.6 cm2
The lateral surface area of a triangular prism is calculated by finding the sum of the areas of the three outer triangles.
First, we calculate the area of the first triangle: (1/2) * base * height = (1/2) * 12 cm * 7.8 cm = 46.8 cm²
Next, we calculate the area of the second triangle: (1/2) * 10 cm * 8 cm = 40 cm²
Finally, we calculate the area of the third triangle: (1/2) * 10 cm * 8 cm = 40 cm²
Adding these three areas together, we get 46.8 cm² + 40 cm² + 40 cm² = 126.8 cm²
Therefore, the lateral surface area of the triangular prism is 126.8 cm².
So, the correct answer is: 126.8 cm2