# In a rectangular prism, the sides of the base are 10cm, 17cm and 21cm, and the height of the prism is 18cm

In a rectangular prism, the sides of the base are 10cm, 17cm and 21cm, and the height of the prism is 18cm, find the cross-sectional area drawn through the side edge and the lower height of the base.

Let us determine the area of the base of the prism by Heron’s theorem.

Savs = √p * (p – AC) * (p – AB) * (p – BC), where p is the semiperimeter of the triangle.

p = (AB + AC + BC) / 2 = (17 + 21 + 10) / 2 = 48/2 = 24 cm.

Sас = √24 * (24 – 21) * (24 – 17) * (24 – 10) = √24 * 3 * 7 * 14 = √7056 = 84 cm2.

The lesser height of a triangle is the height drawn to its larger side.

Then the area of the triangle is also equal to: Savs = AC * BH / 2.

84 = 21 * BH / 2.

BH = 84 * 2/21 = 8 cm.

Determine the cross-sectional area BВ1Н1Н.

S = BH * BB1 = 8 * 18 = 144 cm2.

Answer: The cross-sectional area is 144 cm2.

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