The apothem of a regular quadrangular pyramid is 10 cm, and the area of its base is 16 cm. “2. Find the area of the lateral surface of the pyramid.
In a regular quadrangular pyramid, a square lies at the base. Let us determine the length of the side of the square in terms of the area of the base.
Sbn = СD ^ 2.
СD = √Sbase = √16 = 4 cm.
Apothem SH is the height and median of the isosceles triangle SCD, then the area of the lateral face of the SСD is: Sscd = СD * SH / 2 = 10 * 2/2 = 10 cm2.
Then S side = 4 * Sscd = 4 * 10 = 40 cm2.
Answer: The lateral surface area is 40 cm2.
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