The perimeter of the base of a regular quadrangular pyramid is 12 cm. Find the total surface area
| May 27, 2021 | education
The perimeter of the base of a regular quadrangular pyramid is 12 cm. Find the total surface area of the pyramid if its apothem is 5 cm.
If the perimeter is p = 12 cm, then the side of the square at the base of the pyramid is b = p / 4 = 12/4 = 3 cm.
Side area of the pyramid:
Sb = pa / 2, where a is apothem.
Base area:
Sо = b ^ 2.
Full area S:
S = Sb + So = pa / 2 + b ^ 2 = (12 * 5) / 2 + 3 ^ 2 = 39 cm ^ 2.
Answer: 39 cm ^ 2.
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