The base of the straight prism is a right-angled triangle of the leg of which is 20.21 cm.

| July 17, 2021 | education

The base of the straight prism is a right-angled triangle of the leg of which is 20.21 cm. The large side face of the prism is square. Determine the volume and total surface of the prism.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 400 + 441 = 841.

AC = 29 cm.

The side face of АА1С1С is square, then АА1 = АС = 29 cm.

Determine the area of the base of the prism.

Sbn = AB * BC / 2 = 20 * 21/2 = 210 cm2.

Let us determine the total surface area of the prism.

Sпов = 2 * Sсн * Sside = 2 * 210 + (20 + 21 + 29) * 29 = 2450 cm2.

Let’s define the volume of the prism.

V = Sbn * AA1 = 210 * 29 = 6090 cm3.

Answer: The volume of the prism is 6090 cm3, the area is 2450 cm2.



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