The base of the straight prism is a right-angled triangle with 15 and 20 cm legs. The large side face

univerkov | August 11, 2021 | education

The base of the straight prism is a right-angled triangle with 15 and 20 cm legs. The large side face and the base of the equal-area prism. Find the area of the side and full surface of the prism.

Determine the area of the base of the prism.

Since the triangle ABC is rectangular, then Sosn = AB * BC / 2 = 20 * 15/2 = 150 cm2.

Let us determine the length of the hypotenuse AC of the triangle ABC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 400 + 225 = 625.

AC = 25 cm.

According to the condition Sosn = SАА1С1С, then АС * АА1 = 150 cm2.

AA1 = 150/25 = 6 cm.

Let us determine the area of the lateral surface of the prism.

Side = Ravs * AA1 = (25 + 20 + 15) * 6 = 60 * 6 = 360 cm2.

Answer: The area of the lateral surface of the prism is 360 cm2.

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