Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?
(1 point)
Responses
10 cm
10 cm
17 cm
17 cm
16 cm
16 cm
8 cm
To find the missing length \( l \) of the triangular prism, we first need to calculate the surface area of the prism using the given measurements.
Given:
- Left side of the triangle = 10 cm
- Right side of the triangle = 10 cm
- Perpendicular height from the top vertex to the base = 6 cm
- Base of the triangle = 8 cm
- Surface area = 524 square centimeters
First, calculate the area of the triangular face:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 8 cm * 6 cm
Area of triangle = 24 square centimeters
Since the triangular prism has 2 triangular faces and 3 rectangular faces, the total surface area is:
2 * Area of triangle + 3 * area of rectangle = 524 square centimeters
2 * 24 + 3 * l * 10 = 524
48 + 30l = 524
30l = 476
l = 15.87 cm
Therefore, the missing length \( l \) of the triangular prism is approximately 16 cm. So, the correct answer is:
16 cm