The base of a straight prism is an isosceles triangle with a base of 8 cm

| June 19, 2021 | education

The base of a straight prism is an isosceles triangle with a base of 8 cm and a perimeter of 18 cm. Find the volume of a prism if its two lateral faces are squares.

Let AC be the base of the triangle ABC, then, since the triangle is isosceles, then AB = BC = (Ravs – AC) / 2 = (18 – 8) / 2 = 5 cm.

By condition, the two side faces of the prism are squares, then the height of the prism is 5 cm.

AA1 = BB1 = CC1 = 5 cm.

Let’s construct the height BH of the isosceles triangle ABC, which is also its median. Then AH = CH = AC / 2 = 8/2 = 4 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 16 = 9.

BH = 3 cm.

The area of the base of the prism is equal to: Sbn = АС * ВН / 2 = 8 * 3/2 = 12 cm2.

Then V = Sosn * AA1 = 12 * 5 = 60 cm3.

Answer: The volume of the prism is 60 cm3.



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