Given a regular quadrangular pyramid, the height of which is 12 cm and the apothem is 20 cm. Find the perimeter of the base.
| April 27, 2021 | education
The lateral edges of the pyramid are equal, then the triangle СРD is isosceles, РС = РD, which means that the height of РН will also be the median of the triangle and the apothem of the pyramid.
Apothem РН and the height PO form a right-angled triangle РOН, in which, according to the Pythagorean theorem, we determine the length of the leg OH.
OH ^ 2 = PH ^ 2 – PO ^ 2 = 20 ^ 2 – 12 ^ 2 = 400 – 144 = 256.
OH = 16 cm.
Since the pyramid is regular, there is a square at its base, then the triangle BCD is isosceles, BC = DC, and the OH segment is its middle line, which means BC = 2 * OH = 2 * 16 = 32 cm.
Determine the perimeter of the base.
Ravsd = 4 * BC = 128 cm.
Answer: The perimeter of the base of the pyramid is 128cm.
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