The lateral edge of a regular triangular pyramid is 5 cm, the apothem is 3 cm. Find the area of the base of the pyramid and the height.

univerkov | February 6, 2021 | education

Consider a right-angled triangle SCK with apothem SK = 3 cm and lateral edge SC = 5 cm. By the Pythagorean theorem, we find the leg CK.

CK ^ 2 = CК ^ 2 – СK ^ 2 = 25 – 9 = 16.

CK = 4.

Then the side of the base of the regular pyramid DC = 2 * CK = 2 * 4 = 8 cm.

The base area of the pyramid is equal to: Sbn = 8 * 8 = 64 cm2.

Answer: The base area is 64 cm2.

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