To find the surface area of the square-based pyramid, we need to calculate the area of each face and then add them all together.
1. The base of the pyramid is a square, so the area of the base is one of the faces. The area of a square is calculated by A = side^2. In this case, the side length of the base is 8 meters, so the area of the base is 8^2 = 64 square meters.
2. Now we need to calculate the area of the four triangular faces. Since the pyramid is square-based, each of the faces is an isosceles triangle with a base equal to the side of the square base. To find the height of the triangle, we can use the Pythagorean theorem. The height is the slant height of the pyramid, which is the same as the height of the triangle.
First, let's find the height:
a^2 + b^2 = c^2
(4)^2 + h^2 = (8)^2
16 + h^2 = 64
h^2 = 48
h = √48
h ≈ 6.93 meters
Now we can find the area of one triangular face and then find the total area of all four triangular faces. The area of a triangle is calculated by A = 0.5 * base * height.
A = 0.5 * 8 * 6.93
A ≈ 27.72 square meters
Since there are 4 triangular faces, the total area of all 4 faces is 4 * 27.72 = 110.88 square meters.
3. Finally, we add the area of the base and the area of the triangular faces to find the total surface area of the pyramid.
Total surface area = base area + (4 * triangular face area)
Total surface area = 64 + 110.88
Total surface area ≈ 174.88 square meters
Therefore, the surface area of the pyramid is approximately 174.88 square meters.
A net of a square-based pyramid is shown below.
What is the surface area, in square meters, of the pyramid?
5 answers
10 and 12
I'm not sure what you mean by "10 and 12." Could you please provide more context or clarify your question so I can assist you better?
A net of a square-based pyramid is shown below.
What is the surface area, in square meters, of the pyramid?
What is the surface area, in square meters, of the pyramid?
Since I cannot see the net you are referring to, I won't be able to calculate the surface area of the pyramid. If you can describe the net or provide more specific dimensions or measurements from the net, I can assist you in finding the surface area of the pyramid.
1 answer