What is the shape of the base of a rectangular pyramid?
Rectangle
Vertex
Triangle
Pyramid
Rectangle
What two dimensional shape is created by slicing a right rectangular pyramid perpendicular to the base?
The two dimensional shape created by slicing a right rectangular pyramid perpendicular to the base is a rectangle.
When finding the area of the rectangular pyramid what dimension will be used to find the height of the triangular sides?
8.8 9 6 2
The height of the triangular sides of a rectangular pyramid can be found using the dimension of 9.
Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work
To calculate the surface area of a square pyramid, you need to find the area of the base (which is a square) and the area of the four triangular faces.
Given:
Base length = 12
Slant height = 18
1. Find the area of the base square:
Base area = side length^2
Base area = 12^2 = 144
2. Find the area of each triangular face:
Since it is a square pyramid, each triangular face is an isosceles right triangle. The slant height is the hypotenuse, and the legs are equal to the length of the base side (12).
Using the Pythagorean theorem:
h = sqrt(l^2 + w^2)
h = sqrt(12^2 + 12^2)
h = sqrt(144 + 144)
h = sqrt(288)
h ≈ 16.97
3. Calculate the area of one triangular face:
Area of one triangular face = 0.5 * base * height
Area of one triangular face = 0.5 * 12 * 16.97
Area of one triangular face ≈ 101.82
4. Calculate the surface area of the square pyramid:
Surface area = Base area + 4 * Area of one triangular face
Surface area = 144 + 4 * 101.82
Surface area = 144 + 407.28
Surface area = 551.28
Therefore, the surface area of the square pyramid is approximately 551.28 square units.