Answer:
The total surface area of the pyramid is 2500 sq. cm.
Explanation:
To find the total surface area of a square-based pyramid, you need to find the area of the base and the four lateral faces and add them together.
The area of the base of the pyramid is given as 100 sq. cm., and the vertical height of the pyramid is given as 12 cm. To find the area of each lateral face, you can use the formula for the area of a triangle, which is:
area = (base * height) / 2
Since the base of each lateral face is a rectangle with a length equal to the side length of the square base of the pyramid and a height equal to the vertical height of the pyramid, you can use this formula to find the area of each lateral face.
Therefore, the total surface area of the pyramid is:
total surface area = (4 * ((100 cm^2 * 12 cm) / 2)) + 100 cm^2
= (4 * 600 cm^2) + 100 cm^2
= 2400 cm^2 + 100 cm^2
= 2500 cm^2
So the total surface area of the pyramid is 2500 sq. cm.