The surface area of a triangular prism is given by the formula:
Surface Area = 2(area of base) + (perimeter of base) * (height)
First, we need to calculate the area of the triangular base. The base is a triangle with sides of 8 cm, 6.9 cm, and 8 cm. To calculate the area of a triangle given the lengths of the sides, we can use Heron's formula:
s = (8 + 6.9 + 8) / 2 = 11.95 cm
Area of triangle = √(11.95 * (11.95 - 8) * (11.95 - 6.9) * (11.95 - 8)) ≈ 29.5 cm²
Now we calculate the perimeter of the base:
Perimeter of base = 8 + 6.9 + 8 = 22.9 cm
And the height of the prism is 6 cm.
Now plug these values into the surface area formula:
Surface Area = 2(29.5) + 22.9 * 6
Surface Area = 59 + 137.4
Surface Area ≈ 196.4 cm²
Therefore, the surface area of the triangular prism is approximately 196.4 cm².
8 cm
8 cm
6.9 cm
8 cm
6 cm
What is the surface area of the triangular prism? Round the answer to the nearest tenth.
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