Pyramids
A pyramid is a An object with width, height and depth, eg a cube. shape which can have differently shaped bases. Its sides are triangles which meet at the top.
The most common pyramids are square-based, rectangular-based and triangular-based pyramids.
Volume
The volume of a pyramid can be calculated using the formula:
\(\text{volume of a pyramid} = \frac{1}{3} \times \text{area of base} \times \text{perpendicular height}\)
The If the angle between two lines is a right angle, the lines are said to be perpendicular. height (h) is the height of the pyramid measured at a right angle from the base.
Surface area
The surface area of a pyramid can be calculated by adding the area of the base to the sum of the areas of the triangular faces. If the base of the pyramid is a regular polygon, each of the triangular faces will be identical, so the total area of the triangular faces can be calculated by finding the area of one face and multiplying by the number of triangular faces.
Question
Find the area of this square-based pyramid:
The area of the base is \(5 \times 5 = 25cm^2\)
The area of each triangular face is \((5 \times 6) \div 2 = 15cm^2\).
There are four identical triangular faces, so the total surface area is \(25 + 4 \times 15 = 85cm~^2\)