The base side of a regular triangular prism is 6 cm and the diagonal of the side face is 10 cm
| August 28, 2021 | education
The base side of a regular triangular prism is 6 cm and the diagonal of the side face is 10 cm, find the surface area of the prism.
On the diagonal of the side face and the side of the base, we find the height of the prism:
h = √ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = √64 = 8;
The side face area is 6 * 8 = 48;
The height of the triangle-base of the prism is √ (36 – 9) = √27 = 3√3;
The base area is (6 * 3√3) / 2 = 9√3;
The surface area of the prism is 48 * 3 + 9√3 = 144 + 9√3 ≈ 144 + 9 * 1.733 ≈ 159.6
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