Mastering Surface Area of Pyramids

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Mastering Surface Area of Pyramids

What do you already know about the surface area of 3D shapes?

Learning Objective

At the end of the lesson, you will be able to derive and apply the surface area formula for pyramids with triangular, square, and rectangular bases and solve IGCSE exam-style problems.

What is a Pyramid?

A pyramid is a 3D shape with a polygon base and triangular faces meeting at a common vertex. Bases can be triangle, square, or rectangle.

Surface Area: The Concept

Lateral Area

The sum of the areas of all the triangular faces around the base.

The area of the shape at the bottom of the pyramid (triangle, square, or rectangle).

Base Area

Surface Area Formula: Square Base

Surface Area = (Base Area) + (Area of 4 Triangular Faces) Base Area = side × side Each triangle: 0.5 × base × slant height

Surface Area Formula: Rectangular Base

Surface Area = (length × width) + (Area of 2 Triangular pairs) Each pair shares slant heights based on the rectangle's sides.

Surface Area Formula: Triangular Base

Surface Area = (Area of triangle base) + (Sum of 3 lateral faces) Find area of each triangle using side and slant height.

IGCSE Past Paper Practice

1. Find the surface area of a square-based pyramid with base 6 cm and slant height 8 cm. 2. A rectangular-based pyramid has base 4 cm × 8 cm, slant heights 7 cm and 10 cm. Find its surface area.

Reflection

How confident do you feel about applying the surface area formula to any pyramid? Write down one thing you learnt today.

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.