What is the surface area of a pyramid with a base of 7cm and height of 9.1cm?
To find the surface area of a pyramid, you need to calculate the area of the base and the lateral area.
1. Start by calculating the area of the base. Since the base of the pyramid is a square, you can use the formula for the area of a square, which is side length squared. In this case, the side length is 7 cm, so the area is 7 cm * 7 cm = 49 cm^2.
2. Next, calculate the lateral area of the pyramid. The lateral area is the sum of the areas of the four triangular faces. To find the area of a triangle, you can use the formula: 1/2 * base * height. In this case, the base of each triangle is the side length of the base, which is 7 cm, and the height is the height of the pyramid, which is 9.1 cm. So, the area of each triangle is 1/2 * 7 cm * 9.1 cm = 31.85 cm^2.
3. Since a pyramid has four triangular faces, the total lateral area is 4 * 31.85 cm^2 = 127.4 cm^2.
4. Finally, add the area of the base and the lateral area together to find the total surface area. In this case, the surface area of the pyramid is 49 cm^2 + 127.4 cm^2 = 176.4 cm^2.
Therefore, the surface area of the pyramid with a base of 7 cm and height of 9.1 cm is 176.4 cm^2.