Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
Solve for the surface area of the triangular prism.
(1 point)
Responses
180 square centimeters
180 square centimeters
260 square centimeters
260 square centimeters
280 square centimeters
280 square centimeters
320 square centimeters
320 square centimeters
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page 15 of 15
To find the surface area of the triangular prism, we need to calculate the area of each individual face and add them together.
1. Area of the front triangular face:
Since the triangle is isosceles, we can divide it into two right-angled triangles. The base of each right-angled triangle is 5 cm (half of the total base of 10 cm) and the perpendicular height is 8 cm.
Area of one right-angled triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 square cm
Since there are two right-angled triangles, the total area of the front face = 2 * 20 = 40 square cm
2. Area of the back triangular face:
This is the same as the front triangular face, so the area = 40 square cm
3. Area of the rectangular face:
The width is 6 cm and the height is 8 cm. Area = length * width = 6 * 8 = 48 square cm
Adding all three areas together:
Total surface area = front triangular face + back triangular face + rectangular face
Total surface area = 40 + 40 + 48 = 128 square cm
Therefore, the surface area of the triangular prism is 128 square centimeters.