surface area of pyramids practice connexus answers
1. A square pyramid has a base side length of 8 cm and a slant height of 10 cm. Find the surface area.
First, calculate the area of the base:
Area of base = side length^2
Area of base = 8 cm^2
Area of base = 64 cm^2
Next, calculate the area of the 4 triangular faces:
Area of each triangular face = 0.5 * base * height
Area of each triangular face = 0.5 * 8 cm * 10 cm
Area of each triangular face = 40 cm^2
Total area of 4 triangular faces = 4 * 40 cm^2
Total area of 4 triangular faces = 160 cm^2
Finally, calculate the total surface area:
Total surface area = area of base + total area of 4 triangular faces
Total surface area = 64 cm^2 + 160 cm^2
Total surface area = 224 cm^2
Therefore, the surface area of the square pyramid is 224 cm^2.
2. A triangular pyramid has a base with sides of 6 cm, 8 cm, and 10 cm. The height of the pyramid is 12 cm. Find the surface area.
First, calculate the area of the base triangle using Heron's formula:
S = (a + b + c) / 2
S = (6 cm + 8 cm + 10 cm) / 2
S = 24 cm / 2
S = 12 cm
Area of base triangle = √(S(S-a)(S-b)(S-c))
Area of base triangle = √(12 * (12-6) * (12-8) * (12-10))
Area of base triangle = √(12 * 6 * 4 * 2)
Area of base triangle = √(576)
Area of base triangle = 24 cm^2
Next, calculate the area of the 3 triangular faces:
Area of each triangular face = 0.5 * base * height
Area of each triangular face = 0.5 * 6 cm * 12 cm
Area of each triangular face = 36 cm^2
Total area of 3 triangular faces = 3 * 36 cm^2
Total area of 3 triangular faces = 108 cm^2
Finally, calculate the total surface area:
Total surface area = area of base + total area of 3 triangular faces
Total surface area = 24 cm^2 + 108 cm^2
Total surface area = 132 cm^2
Therefore, the surface area of the triangular pyramid is 132 cm^2.