surface area of pyramids practice connexus
1. Find the surface area of a square pyramid with a base side length of 5 cm and a slant height of 8 cm.
To find the surface area of a square pyramid, we need to calculate the area of the square base and the area of the four triangular faces.
First, calculate the area of the square base:
Area of square base = side length^2
Area of square base = 5 cm ^ 2 = 25 cm^2
Next, calculate the area of one triangular face:
Area of triangular face = (1/2) * base * height
Area of triangular face = (1/2) * 5 cm * 8 cm = 20 cm^2
Since there are four triangular faces on a square pyramid, multiply the area of one triangular face by 4:
Total area of triangular faces = 20 cm^2 * 4 = 80 cm^2
Finally, add the area of the square base and the total area of the triangular faces to find the total surface area of the pyramid:
Surface area = Area of square base + Total area of triangular faces
Surface area = 25 cm^2 + 80 cm^2 = 105 cm^2
Therefore, the surface area of the square pyramid is 105 cm^2.
2. Find the surface area of a triangular pyramid with a base side length of 6 cm, a height of 4 cm, and a slant height of 7 cm.
To find the surface area of a triangular pyramid, we first need to calculate the area of the triangular base and the area of the three triangular faces.
First, calculate the area of the triangular base using the formula for the area of a triangle:
Area of triangular base = (1/2) * base * height
Area of triangular base = (1/2) * 6 cm * 4 cm = 12 cm^2
Next, calculate the area of one triangular face using the formula for the area of a triangle:
Area of triangular face = (1/2) * base * height
Area of triangular face = (1/2) * 6 cm * 7 cm = 21 cm^2
Since there are three triangular faces on a triangular pyramid, multiply the area of one triangular face by 3:
Total area of triangular faces = 21 cm^2 * 3 = 63 cm^2
Finally, add the area of the triangular base and the total area of the triangular faces to find the total surface area of the pyramid:
Surface area = Area of triangular base + Total area of triangular faces
Surface area = 12 cm^2 + 63 cm^2 = 75 cm^2
Therefore, the surface area of the triangular pyramid is 75 cm^2.