The base of the straight prism is an isosceles trapezoid ABCD (BC || AD), BC = 6 cm, AD = 10 cm

| May 21, 2021 | education

The base of the straight prism is an isosceles trapezoid ABCD (BC || AD), BC = 6 cm, AD = 10 cm, angle A 45 degrees. The height of the prism is equal to the side of the trapezoid. Find the area of the lateral surface of the prism.

Consider an isosceles trapezoid that lies at the base of a straight prism.

Let’s build the height BH. The ABH triangle is rectangular and isosceles, since the angle is A = 45, and the angle is H = 90.

The height ВН divides the base AD into two segments, the length of the smaller of which is equal to:

AH = (AD – BC) / 2 = (10 – 6) / 2 = 2 cm.

Then AB = AH / Cos45 = 2 / (√2 / 2) = 2 * √2 cm

Determine the perimeter of the trapezoid.

Ravsd = 2 * AB + BC + AD = 2 * 2 * √2 + 6 + 10 = 4 * √2 + 16 cm.

Then Sprism = Ravsd * h, where h is the height of the prism, which, by condition, is equal to AB.

S = (4 * √2 + 16) * 2 * √2 = 16 + 32 * √2 = 16 * (1 + 2 * √2) cm2.

Answer: The lateral surface area is 16 * (1 + 2 * √2) cm2.



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