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?
17 cm
8 cm
10 cm
16 cm
To find the surface area of a triangular prism, you need to calculate the area of both triangular faces and all three rectangular faces.
1. Area of triangular face:
A = (base * height) / 2
A = (8 * 6) / 2
A = 24 square cm
Since there are two triangular faces, the total area of both triangular faces is 2 * 24 = 48 square cm.
2. Area of rectangular face:
Since the right rectangular face is visible, we need to calculate its area:
A = length * width
A = 10 * l
A = 10l square cm
Since there are two rectangular faces, the total area of both rectangular faces is 2 * 10l = 20l square cm.
3. The total surface area is given as 524 square cm:
524 = 48 + 20l
476 = 20l
l = 23.8 cm
Therefore, the missing length of the triangular prism is 23.8 cm (closest to option 17 cm).