Pyramids
A pyramid is a 3D shape that has a polygon as a base and sloping sides that meet at a point called the apex. If the apex is directly above the centre of the base, the pyramid is called a right pyramid. Pyramids are named according to the shape of their base.
As we found with prisms, calculating the surface area of a pyramid is done by adding the area of all faces and so it is helpful to visualise the net:
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| Regular right-pentagonal pyramid | The net of a regular right-pentagonal pyramid |
For pyramids, the net consists of the base and a number of triangular faces. If the pyramid is a right pyramid and if the base shape is regular (meaning its side lengths are all equal - like a square or equilateral triangle) then all the triangular faces are equivalent. On the other hand if the base is not regular, for example if it is rectangular, then the triangles will have different sizes.
$\text{Surface area of pyramid }=\text{area of base }+\text{area of triangles }$Surface area of pyramid =area of base +area of triangles
Practice questions
question 1
Find the surface area of the square pyramid shown. Include all faces in your calculations.
question 2
QUESTION 3
Some very famous right square pyramids are the Egyptian Pyramids. Pictured here is the Great Pyramid. It has a base of $230$230 m and a slant height of $216$216 m.
Find the surface area of the Great Pyramid. Do not include the base of the pyramid in your calculation.
Question 4
Consider this regular pentagonal pyramid and its net.
How many identical triangular faces does it have?
$\editable{}$ triangular faces.
Find the area of one triangular face.
Find the total surface area of the triangular faces of the pyramid.