The base of a straight prism is a rhombus with diagonals of 16 and 30 cm. The large diagonal of the prism is 50 cm

| April 18, 2021 | education

The base of a straight prism is a rhombus with diagonals of 16 and 30 cm. The large diagonal of the prism is 50 cm. Calculate the area of the lateral surface of the prism.

Since there is a rhombus at the base of the prism, the diagonals AC and BD intersect at right angles and are halved at the point of intersection.

AO = CO = AC / 2 = 30/2 = 15 cm.

BO = DO = BD / 2 = 16/2 = 8 cm.

Let us determine the hypotenuse AD from the right-angled triangle AOD.

AD ^ 2 = AO ^ 2 + DO ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289.

AD = 17 cm.

In a rhombus, all sides are equal, then AB = BC = CD = AD = 17cm.

Consider a right-angled triangle AA1C and, by the Pythagorean theorem, define leg AA1.

AA1 ^ 2 = A1C ^ 2 – AC ^ 2 = 50 ^ 2 – 30 ^ 2 = 2500 – 900 = 1600.

AA1 = 40 cm.

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

Side = 4 * AB * AA1 = 4 * 40 * 17 = 2720 cm2.

Answer: S side = 2720 cm2.



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