Essential Area and Volume Formulas

Area formulas help you calculate the space inside 2D shapes, whilst volume formulas work out how much space 3D objects take up. Think of area as the amount of wrapping paper you'd need, and volume as how much stuff you can actually fit inside!

For 2D shapes, the key ones you'll use are squares (base × height), rectangles (base × height), and triangles (base × perpendicular height ÷ 2). The trapezium formula uses $a+b$ × height ÷ 2, where a and b are the parallel sides.

Parallelograms need base × perpendicular height, while a rhombus uses length × height ÷ 2. For circles, it's simply π × r² - probably the most famous formula you'll ever learn!

Top Tip: Always double-check you're using perpendicular height, not slanted height - this catches loads of students out in exams!

The 3D volume formulas follow similar patterns. Spheres use 4/3 × π × r³, whilst cylinders are π × r² × height. Rectangular prisms are just length × width × height, and cones are 1/3 × π × r² × height. Remember that prisms multiply the base area by height, making calculations much simpler once you've got the base sorted.