A square pyramid has sides of 8 m. Each face is an equilateral triangle.
What is the lateral area of the pyramid?
To find the lateral area of a square pyramid, we need to calculate the sum of the areas of all the triangular faces.
In this case, each face is an equilateral triangle, and we know that the side length of the triangles is 8 m.
The formula to calculate the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side length^2
Substituting the side length of 8 m into the formula, we get:
Area = (sqrt(3) / 4) * 8^2
= (sqrt(3) / 4) * 64
= (1.732 / 4) * 64
= 1.732 * 16
= 27.712
Since there are 4 triangular faces in a square pyramid, the lateral area is:
Lateral Area = 4 * 27.712
= 110.848 square meters.
Therefore, the lateral area of the pyramid is 110.848 square meters.
To find the lateral area of a square pyramid, you need to calculate the combined area of all the triangular faces excluding the base.
In this case, each face of the pyramid is an equilateral triangle. The formula to find the area of an equilateral triangle is given by:
Area = (√3 / 4) * side^2
Given that the side of the equilateral triangle is 8 m, we can substitute it in the formula to find the area of one triangular face:
Area of one triangular face = (√3 / 4) * (8^2)
Simplifying this equation:
Area of one triangular face = (√3 / 4) * 64
Area of one triangular face = 16√3
Since a square pyramid has four faces, to find the total lateral area, we multiply the area of one face by four:
Lateral area of the pyramid = 4 * 16√3
Lateral area of the pyramid = 64√3 square meters
Therefore, the lateral area of the square pyramid with sides of 8 m is 64√3 square meters.
An equilateral triangle of side s has area √3/2 s^2
You have four triangles of side 8.
A square pyramid has sides of 8 m. Each face is an equilateral triangle.
What is the lateral area of the pyramid?