The base of a straight prism is a square. the diagonal of the prism is 10 cm, and its height is 6 cm

| June 14, 2021 | education

The base of a straight prism is a square. the diagonal of the prism is 10 cm, and its height is 6 cm. Find the area of the lateral surface of the prism and its volume.

The diagonal of the prism, the height of the prism and the diagonal of the base make up a right triangle (the height is perpendicular to the base). Find the diagonal of the base by the Pythagorean theorem: √ (10² – 6²) = √ (100 – 36) = √64 = 8 cm.

At the base of the prism lies a square, let its side be equal to a, then by the Pythagorean theorem:

a² + a² = 8².

2а² = 64.

a² = 32.

a = √32 = 6√2 cm.

The lateral surface area is equal to the sum of the two base areas and the lateral surface area.

Sb = 6√2 * 6√2 = 72 cm².

The side surface is 4 equal rectangles.

Side = (6√2 * 6) * 4 = 144√6 cm².

Sp = 72 * 2 + 144√6 = 144 + 144√6 (cm²).

The volume of the prism is: V = Sbn * h = 72 * 6 = 432 (cm3).



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