In a regular triangular prism, the side rib is 18 mm long and the base side is 24 mm. Find the perimeter of the section drawn

| September 9, 2021 | education

In a regular triangular prism, the side rib is 18 mm long and the base side is 24 mm. Find the perimeter of the section drawn through the side of the bottom base and the opposite vertex of the top base.

Consider a right-angled triangle AA1C, whose leg AA1C is equal to the height of the prism, and leg AC is equal to the side of the triangle at the base of the prism.

By the Pythagorean theorem A1C ^ 2 = AA1 ^ 2 + AC ^ 2 = 18 ^ 2 + 24 ^ 2 = 324 + 576 = 900.

A1C = 30 cm.

Section CA1B is an isosceles triangle with base CB = 24 cm, and sides A1C and A1B = 30 cm.

Let’s find the height A1D of the section CA1B.

A1D ^ 2 = A1C ^ 2 – CD ^ 2 = 30 ^ 2 – (24/2) ^ 2 = 900 – 144 = 756 = 6 * √21.

Then Sa1cw = (CB * A1D) / 2 = (24 * 6 * √21) / 2 = 72 * √21.

Answer: Sa1cw = 72 * √21 cm2.



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