Use the image to answer the question.
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 8 centimeters. The left side meets the base to form a right angle. The base of the triangle measures 6 centimeters. The hypotenuse side of the triangle measures 10 centimeters. The width of the rectangular face measures 9 centimeters.
What is the surface area of the triangular prism?
(1 point)
square centimeters
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To calculate the surface area of the triangular prism, we need to find the area of each face and then add them together.
First, we find the area of the triangular base:
Area = (1/2) * base * height
Area = (1/2) * 6 cm * 8 cm
Area = 24 square cm
Now, we find the area of the rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 square cm
Since there are two triangular faces and three rectangular faces, we need to calculate the total surface area by adding all five areas together:
Total Surface Area = 2*(Area of triangular base) + 3*(Area of rectangular face)
Total Surface Area = 2*(24 square cm) + 3*(90 square cm)
Total Surface Area = 48 square cm + 270 square cm
Total Surface Area = 318 square cm
Therefore, the surface area of the triangular prism is 318 square centimeters.