# The basis of a straight prism is an isosceles triangle with a base of 8 cm and a lateral side of 5 cm.

The basis of a straight prism is an isosceles triangle with a base of 8 cm and a lateral side of 5 cm. The height of the prism is equal to the lower height of the base. Find the volume of the prism.

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

The semi-perimeter of the triangle is: p = (AB + BC + СD) / 2 = (8 + 5 + 5) / 2 = 9 cm.

Sb = √9 * (9 – 8) * (9 – 5) * (9 – 5) = √144 = 12 cm2.

Let us determine the length of the CH height.

Sosn = AB * CH / 2.

СН = 2 * Sosn / AB = 2 * 12/8 = 3 cm.

Let us determine the length of the height of the AK.

Sosn = BC * AK / 2.

AK = 2 * Sbn / BC = 2 * 12/5 = 4.8 cm.

СK <AK, then the height of the prism is 3 cm.

Let’s define the volume of the prism.

V = Sbn * AA1 = 12 * 3 = 36 cm3.

Answer: The volume of the prism is 36 cm3.

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