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
17 cm
17 cm
10 cm
10 cm
16 cm
16 cm
8 cm
8 cm
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To find the missing length \(l\), we first need to calculate the total surface area of the triangular prism.
Total Surface Area = (2 * Area of front triangular face) + (3 * Area of rectangular face)
The front triangular face area can be calculated as:
\(\frac{1}{2} * base * height = \frac{1}{2} * 8 * 6 = 24 \, cm^2\)
The rectangular face area can be calculated as:
\(length * width = l * 10\)
Adding the areas together:
Total Surface Area = (2 * 24) + (3 * l * 10) = 48 + 30l
Given that the total surface area is 524 square centimeters, we have:
48 + 30l = 524
30l = 476
l = 15.87
Therefore, the missing length \(l\) of the triangular prism is approximately 16 cm.
So the correct answer is:
16 cm.