# 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.