The Formulae (Leaving Cert Mathematics): Revision Notes

The Formulae

What are Formulae in Area and Volume?

Mathematics provides us with formulae to calculate the area and volume of various 2D and 3D shapes. These are essential tools for solving problems in geometry and real-life applications.

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Common Area Formulae

Rectangle/Square:

• Area $= \text{length} \times \text{width}$

Triangle:

• Area $= \frac{1}{2} \times \text{base} \times \text{height}$

Circle:

• Area $= \pi r^2$, where $r$ is the radius.

Parallelogram:

• Area $= \text{base} \times \text{height}$

Trapezium:

• Area $= \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$

Sector of a Circle:

• Area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle in degrees.

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Common Volume Formulae

Rectangular Prism (Cuboid):

• Volume $= \text{length} \times \text{width} \times \text{height}$

Cylinder:

• Volume $= \pi r^2 h$, where $h$ is the height.

Sphere:

• Volume $= \frac{4}{3} \pi r^3$

Cone:

• Volume = $\frac{1}{3} \pi r^2 h$

Triangular Prism:

• Volume = $\text{Area of Base} \times \text{height}$

Pyramid:

• Volume = $\frac{1}{3} \times \text{Base Area} \times \text{height}$

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Worked Examples

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Summary

• Area Formulae:
  • Rectangle: $\text{length} \times \text{width}$
  • Triangle: $\frac{1}{2} \times \text{base} \times \text{height}$
  • Circle: $\pi r^2$
• Volume Formulae:
  • Cylinder: $\pi r^2 h$
  • Sphere: $\frac{4}{3} \pi r^3$
  • Cone: $\frac{1}{3} \pi r^2 h$
• Memorise and apply these formulas to solve geometry problems effectively.