At the base of a straight prism lies an isosceles triangle with a base of 12 cm and a lateral side of 10 cm

At the base of a straight prism lies an isosceles triangle with a base of 12 cm and a lateral side of 10 cm. Find the volume of the prism, the diagonal of the smallest lateral face is 26 cm.

In an isosceles triangle ABC, we draw the height of BH, which is also the median of the triangle, then CH = BH = BC / 2 = 12/2 = 6 cm.

By the Pythagorean theorem, we determine the length of the height AH. AH^2 = AC^2 – CH^2 = 100 – 36 = 64.

AH = 8 cm.

From the right-angled triangle ABB1 we define the leg BB1.

BB1^2 = AB1^2 – AB^2 = 676 – 100 = 576.

BB1 = 24 cm.

Determine the area of the base of the prism.

Sb = ВС * АН / 2 = 12 * 8/2 = 48 cm2.

Let’s define the volume of the prism.

V = Sbn * BB1 = 48 * 24 = 1152 cm3.

Answer: The volume of the prism is 1152 cm3.