# In a straight triangular prism, the sides of the base are 9cm, 12cm and 15cm. prism height 10cm. find the cross-sectional

In a straight triangular prism, the sides of the base are 9cm, 12cm and 15cm. prism height 10cm. find the cross-sectional area drawn through the side rib and the large height of the base.

By Heron’s theorem, we determine the area of the triangle at the base of the prism.

Sosn = √р * (р – AB) * (р – ВС) * (р – АС), where р is the base semiperimeter.

P = (AB + BC + AC) / 2 – (12 + 9 + 15) / 2 = 38/2 = 18 cm.

Sb = √18 * (18 – 12) * (18 – 9) * (18 – 15) = √18 * 6 * 9 * 3 = √2916 = 54 cm2.

The diseased base height is the height drawn to the lesser side.

Then the base area will also be equal to:

Sosn = AH * BC / 2 = AH * 9/2 = 54.

AH = 54 * 2/9 = 12 cm.

Since the prism is straight, the section АА1Н1Н is a rectangle, and its area will be equal to:

Scche = AA1 * AH = 10 * 12 = 120 cm2.

Answer: The cross-sectional area is 120 cm2.

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