To find the surface area of a triangular prism, we need to calculate the area of each face and then sum them up.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area of the triangle) + (perimeter of the base)*(height) + (area of the two triangular faces)
In this case, the base of the triangular prism is a right-angled triangle with base = 3 cm and height = 4 cm.
1. Calculate the area of the base triangle:
Base Area = 0.5 * base * height
Base Area = 0.5 * 3 cm * 4 cm = 6 cm^2
2. Calculate the perimeter of the base:
Perimeter = sum of all sides = 3 cm + 4 cm + 5 cm = 12 cm
3. Calculate the area of the two triangular faces:
Triangle Area = 0.5 * base * height
Triangle Area = 0.5 * 3 cm * 4 cm = 6 cm^2
Total Triangle Area = 2 * 6 cm^2 = 12 cm^2
4. Calculate the surface area of the prism:
Surface Area = 2 * (6 cm^2) + (12 cm) * (4 cm) + 12 cm^2
Surface Area = 12 cm^2 + 48 cm^2 + 12 cm^2
Surface Area = 72 cm^2
Therefore, the surface area of the triangular prism is 72 square centimeters rounded to the nearest tenth.
Surface Area of Triangular Prisms Practice
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What is the surface area of the triangular prism? Round the answer to the nearest tenth.
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