Explanation:
The lateral surface area of a regular pyramid is equal to the product of its base area and a factor dependent on its slope. The total surface area of the pyramid is equal to the sum of its lateral surface area and the area of its base.
For a pyramid with a base of 10 cm and a height of 12 cm, the lateral surface area can be determined by first calculating the area of its base:
Base Area = (1/2)*(10 cm)*(10 cm) = 50 cm^2.
The factor dependent on the slope is then calculated using the following formula: Slope Factor = (1/2)*sqrt((h^2) + (a^2)), where h is the height and a is the side length of the base.
Slope Factor = (1/2)*sqrt((12 cm)^2 + (10 cm)^2) = (1/2)*14 cm = 7 cm.
Thus, the lateral surface area of the pyramid is equal to the product of the base area and the slope factor: Lateral Surface Area = (50 cm^2)*(7 cm) = 350 cm^2.
The total surface area of the pyramid is equal to the sum of its lateral surface area and the area of its base: Total Surface Area = 350 cm^2 + 50 cm^2 = 400 cm^2.