Summary (Grade 11 NSC Matric Mathematics): Revision Notes

Summary

What is area?

Area measures the amount of flat surface space contained within the boundaries of a 2D shape. Think of it as how much paint you would need to cover a flat surface completely.

Area formulae for common shapes

Understanding how to calculate area is essential for solving measurement problems. Here are the key formulae you need to memorise:

• Square: $A = s^2$ (where $s$ is the side length)
• Rectangle: $A = b \times h$ (where $b$ is breadth and $h$ is height)
• Triangle: $A = \frac{1}{2}b \times h$ (where $b$ is base and $h$ is height)
• Trapezium: $A = \frac{1}{2}(a + b) \times h$ (where $a$ and $b$ are parallel sides, $h$ is height)
• Parallelogram: $A = b \times h$ (where $b$ is base and $h$ is perpendicular height)
• Circle: $A = \pi r^2$ (where $r$ is the radius)

What is surface area?

Surface area represents the total area of all the exposed outer surfaces of a 3D object or prism. Imagine wrapping a present - the surface area is the total amount of wrapping paper you would need.

What is a net?

A net is the unfolded flat pattern of a 3D solid. When you cut along the edges of a 3D shape and flatten it out, you create its net. This helps us visualise and calculate surface areas.

The diagram above shows different possible nets for a cube. Each arrangement can be folded to form a complete cube.

What is volume?

Volume measures the amount of 3D space occupied by an object, or alternatively, how much the object can contain. Think of it as how much water could fill a container.

Volume formulae for prisms and basic solids

• Rectangular prism: $V = l \times b \times h$ (length × breadth × height)
• Triangular prism: $V = (\frac{1}{2}b \times h) \times H$ (area of triangle × height of prism)
• Square prism (cube): $V = s^3$ (side length cubed)
• Cylinder: $V = \pi r^2 \times h$ (area of circular base × height)

What is a pyramid?

A pyramid is a 3D geometric solid that has a polygon as its base. All the triangular sides meet at a single point called the apex. The sides are not perpendicular to the base, which distinguishes pyramids from prisms.

Surface area formulae for pyramids and curved solids

• Square pyramid: $SA = b(b + 2h_s)$ (where $b$ is base side, $h_s$ is slant height)
• Triangular pyramid: $SA = \frac{1}{2}b(h_b + 3h_s)$ (where $h_b$ is base height, $h_s$ is slant height)
• Right cone: $SA = \pi r(r + h_s)$ (where $r$ is radius, $h_s$ is slant height)
• Sphere: $SA = 4\pi r^2$ (where $r$ is radius)

Volume formulae for pyramids and curved solids

All pyramid volumes use the same principle: one-third of the base area multiplied by the perpendicular height.

• Square pyramid: $V = \frac{1}{3} \times b^2 \times H$ (where $b$ is base side, $H$ is perpendicular height)
• Triangular pyramid: $V = \frac{1}{3} \times \frac{1}{2}bh \times H$ (where $bh$ is base area, $H$ is perpendicular height)
• Right cone: $V = \frac{1}{3} \times \pi r^2 \times H$ (where $r$ is radius, $H$ is perpendicular height)
• Sphere: $V = \frac{4}{3}\pi r^3$ (where $r$ is radius)