What is the area of the lateral surface of a regular quadrangular pyramid with a side at the base of 4.5 cm

What is the area of the lateral surface of a regular quadrangular pyramid with a side at the base of 4.5 cm and an apothem of 5 cm?

Since the pyramid is regular, at its base lies a square with a side of 4.5 cm. The lateral faces of a regular pyramid are equilateral triangles, then the apothem O1H of the pyramid is the height and median of the isosceles triangle СDO1. Then the area of the triangle СDO1 will be equal to: Scdo1 = СD * O1H / 2 = 4.5 * 5/2 = 11.25 cm2.

Since the side faces of the regular pyramid are of equal size, then Sside = 4 * Sdo1 = 4 * 11.25 = 45 cm2.

Answer: B) The lateral surface area is 45 cm2.