Surface Area of a Regular Pyramid
How to find the surface area of a regular pyramid: definition of a pyramid and its parts, formula, proof, examples, and its solution.
This shape is called a pyramid.
A pyramid has one base and a vertex.
The height is the distance
between the base's plane and the vertex.
The lateral faces of a prism are the faces
that are not the base.
A regular pyramid is a pyramid
whose base is a regular polygon.
The height of a regular pyramid
meets with the center of the base.
The slant height of a regular pyramid
is the height of the lateral face.
A = B + (1/2)Phs
A: surface area of a regular pyramid
B: base area
P: perimeter of the base
hs: slant height of the regular pyramid
(1/2)Phs: lateral area
Draw the net of a regular pyramid.
Set the side of the base as a.
The base area is B.
See the lateral faces in the net.
Each lateral face is a triangle
whose base is a.
For an n-gon base,
there are n of those triangles.
So P = a⋅n.
The lateral area is formed by n of triangles.
So the lateral area is (1/2)ahs⋅n.
Area of a triangle
Then A = B + (1/2)ahs⋅n.
P = a⋅n
So A = B + (1/2)Phs.
To use the formula,
find B, P and hs.
To find hs,
draw a right triangle
that includes the height and the slant height.
It's legs are 5 (= 10/2) and 12.
So this is a (5, 12, 13) triangle.
So hs = 13.
B = 102 = 100
Area of a square
P = 10⋅4 = 40
B = 100, P = 40, hs = 13
A = 100 + (1/2)⋅40⋅13