Area of rectangles and triangles

Objective. Derive and apply area formulae.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

The area of a shape measures the amount of surface it covers, expressed in square units such as cm². For a rectangle, area is found using A=l×w, multiplying the length by the width. For a triangle, the area formula is A=½×b×h, where b is the base and h is the perpendicular height, since a triangle covers exactly half the area of a rectangle with the same base and height. For example, a triangle with base 8 cm and height 5 cm has area ½×8×5=20 cm².

Worked example

Find the area of a triangle with a base of 12 cm and a perpendicular height of 7 cm.

1 $Recall the formula for the area of a triangle: A=½\timesb\timesh.$
2 $Substitute the values: A=½\times12\times7.$
3 $Calculate 12\times7=84.$
4 $Halve the result: 84\div2=42.$

Answer: 42 cm²

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Common mistake. Pupils often forget to halve the result when finding the area of a triangle, calculating base×height without the factor of a half. Always include the ½ when applying the triangle area formula.

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