Pyramids
A pyramid is a An object with width, height and depth, eg a cube. solid with flat A plane surface of a geometric solid. A cube has 6 faces; a tetrahedron, 4 faces.. The base of a pyramid is a polygon and is used to describe the pyramid (eg a square-based pyramid, triangle-based pyramid etc). Its sides are triangles which meet at the top.
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. (This is not to be confused with the slant height which is one edge from the base to the top vertex.)
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.
Question
Find the area of this square-based pyramid. Note that the slant height is 6cm.
The area of the base is \(5 \times 5 = 25~cm^2\).
The area of each triangular face is \((5 \times 6) \div 2 = 15~cm^2\).
There are four identical triangular faces, so the total surface area is \(25 + 4 \times 15 = 85~cm^2\).