- A pyramid is a three-dimensional solid with a polygonal base and flat triangular (lateral) faces that meet at a point called the apex.
- The height or altitude of the pyramid is the line drawn from the apex perpendicular to the base.
- A pyramid is named after the shape of its base. Here are a few different types of pyramids.
- Pyramids can further be classified as regular pyramids and irregular pyramids.
- In a regular pyramid, the base is a regular polygon (all sides are equal), and all the lateral faces are triangles.
- The height of each triangle of a regular pyramid is the slant height of the pyramid.
Volume of Triangular Pyramids
- The volume of a regular pyramid with the area of the base and height can be calculated using the formula mentioned below.
Surface Area of Triangular Pyramids
- A regular triangular pyramid has a triangular base (all sides equal) and three triangular lateral faces.
- The lateral area of a regular pyramid can be found by adding the area of lateral faces.
, where the perimeter of the base, and the slant height of the triangular faces.
- The total area of a triangular prism can be found by adding an area of the base and the area of lateral faces.
Volume of Square Pyramids
- The volume of a square pyramid with the area of base and height can be calculated using the formula mentioned below.
Surface Area of Square Pyramids
- A square pyramid has a square base and four triangular lateral faces.
- The lateral surface area of a square pyramid with a perimeter of the base and slant height can be calculated using the formula mentioned below:
- The total surface area of a square pyramid:
Some Solved Examples
Question 1: A square pyramid has a side length of 6 cm and a height of 10 cm. Find the volume of the square pyramid.
Question 2: The base of a triangular pyramid is an equilateral triangle with a side length of 12 units. If the height of the base triangle is 10 units and the slant height is 11 units, find the total surface area of the pyramid.
- For any regular pyramid with the area of the base , height , slant height of the base , and perimeter of the base :
- Lateral Surface Area,
- Total Surface Area,
- It is essential to know how to find the base's area based on the polygon's shape.
- Sometimes students get confused between a pyramid's slant height and altitude (height).
- Fiona Wong
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