# At the base of the straight prism there is a rhombus with diagonals of 12 cm and 16 cm.

September 29, 2021 | education

| **At the base of the straight prism there is a rhombus with diagonals of 12 cm and 16 cm. The total surface area of the prism is 472 cm2. Find the side edge and the edge of the base of the prism.**

Determine the area of the base of the prism. Sb = 12 * 16/2 = 96 cm2.

Then Sside = Sпов – 2 * Sсн = 472 – 2 * 96 = 280 cm2.

Let us define the side of the base of the rhombus by the Pythagorean theorem.

The diagonals of the rhombus are halved at the intersection. Then AB ^ 2 = 6 ^ 2 + 8 ^ 2 = 100. AB = 10 cm.

Determine the perimeter of the base P = 4 * 10 = 40 cm.

Sside = P * h.

h = S side / P = 280/40 = 7 cm.

Answer: The side edge of the prism is 7 cm, the side of the base is 10 cm.

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