The height of a regular quadrangular pyramid is 10 cm. The lateral edge of the pyramid is inclined to the base

| August 3, 2021 | education

The height of a regular quadrangular pyramid is 10 cm. The lateral edge of the pyramid is inclined to the base plane at angles of 45 degrees. What is the area of the base of the pyramid?

Consider a rectangular triangle AO1O, whose angle OAO1, by condition, is equal to 45.

Let us determine the length of the leg AO1, which is half the length of the diagonal AC of the base of the pyramid.

tgA = OO1 / AO1.

tg45 = 10 / AO1.

AO1 = 10/1 = 10 cm.

Then the diagonal AC = 2 * AO1 = 2 * 10 = 20 cm.

Consider a right-angled triangle ACD.

By the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 2 * AD ^ 2.

AD = AC / √2 = 10 / √2.

Then, the area of the base of the pyramid is equal to: Sbn = АD ^ 2 = (10 * √2) = 200 cm2.

Or Sbn = AC ^ 2/2 = 400/2 = 200 cm2.

Answer: Sbn = 200 cm2.



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