At the base of a straight prism lies a rhombus with diagonals 10 and 24, its surface area is 292

| June 9, 2021 | education

At the base of a straight prism lies a rhombus with diagonals 10 and 24, its surface area is 292 find the lateral edge of this prism.

Determine the area of ​​the base of the prism.

Sbn = A1C1 * B1D1 / 2 = 24 * 10/2 = 120 cm2.

Let us determine the area of ​​the lateral surface of the prism.

Sside = Sпов – 2 * Sсн = 292 – 240 = 52 cm2.

The diagonals of the rhombus lying at the base of the prism are divided in half at the point of intersection and intersect at right angles, then A1O = A1C1 / 2 = 24/2 = 12 cm, B1O = B1D1 / 2 = 10/2 = 5 cm.

Then in a right-angled triangle A1B1O, A1B12 = A1O ^ 2 + B1O ^ 2 = 144 + 25 = 169.

A1B1 = 13 cm.

Determine the perimeter of the base of the prism. Since all sides of a rhombus are equal, Rosn = 4 * A1B1 = 4 * 13 = 52 cm.

Determine the heights of the prism.

Sside = АА1 * Rusn.

AA1 = S side / Rosn = 52/52 = 1 cm.

Answer: The side edge of the prism is 1 cm.



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