Wize High School Geometry Textbook (Common Core) > 3D Measurements

Surface Area & Volume of a Right Pyramid

Popular Courses

US High School

0:00 / 0:00

Surface Area of a Right Pyramid
A right pyramid is a solid 3D object with a base that is a regular polygon (all side lengths are the same), and with a vertex that is directly above the center of the base. 
Surface Area
The surface area of a right pyramid can be broken down into the following:
Area of the base

Since this is a regular polygon, we can calculate the area by breaking it up into equal triangles
Area of the triangular sides

Each trigular side=Side length of polygon×Slant height2\text{Each trigular side}=\dfrac{\text{Side length of polygon}\times\text{Slant height}}{2}Each trigular side=2Side length of polygon×Slant height​
To find the surface area, we add up the area of the base and the area of the triangular sides.

Square-Based Pyramid
The surface area of a square-based pyramid with base side length bbb and a slant height of LLL is
S.A.square-based pyramid=b2+2bL\large\boxed{\text{S.A.}_\text{square-based pyramid}=b^2+2bL}S.A.square-based pyramid​=b2+2bL​

Practice: Surface Area of a Right Pyramid
What is the surface area of the following right pyramid?

Enter the surface area of this right pyramid in

m^2

rounded to 2 decimal places, do not include units

I don't know

0:00 / 0:00

Volume of a Right Pyramid
The volume of a right pyramid is 13\dfrac{1}{3}31​ the volume of the prism with the same base and the same height.

Vpyramid=13(Area of the base×height)\large\boxed{V_\text{pyramid}=\dfrac{1}{3}\left(\text{Area of the base}\times \text{height}\right)}Vpyramid​=31​(Area of the base×height)​

Practice: Volume of a Right Pyramid
What is the volume of the following right pyramid?

Enter the volume in

m^3

, do not include units

I don't know

Practice: Right Pyramid
A right pyramid has a base that is a regular hexagon (6-sided polygon) with side length 10 cm and base area of 150 cm2. The height of the pyramid is 12 cm.

a) Determine the slant height of the pyramid.

b) Determine the surface area of the pyramid.

c) Determine the volume of the pyramid.

a) Enter the slant height of the pyramid in

cm

b) Enter the surface area of the pyramid in

cm^2

c) Enter the volume of the pyramid in

cm^3

I don't know

Practice: Right Pyramid
A fish tank company has 2 new designs -- a rectangular-base prism tank and a regular octagonal-base (8 sided polygon) pyramid tank. The dimensions of the tank are shown in this diagram.

The volumes of the two tanks are to be equal, and both tanks are to be produced using the same glass material. Which tank will require less glass to produce?

A) The rectangular-base prism tank

B) The octagonal-base pyramid tank

C) Both tanks will require the same amount of glass to produce

I don't know