Area of triangles

Finding the area of triangles is a fundamental geometry skill that appears throughout GCSE Mathematics. The standard formula works for all triangles, regardless of their type. **The Formula:** Area = ½ × base × perpendicular height or Area = (base × height) ÷ 2 **Key Points:** - The height must be PERPENDICULAR (at 90°) to the base - Any side can be chosen as the base - The height might be inside OR outside the triangle - For right-angled triangles, the two shorter sides can be used as base and height **Finding the Height:** - In right-angled triangles: use the two sides that meet at 90° - In other triangles: look for a height line drawn perpendicular to the base - Sometimes you need to use Pythagoras' theorem to find the height **Units:** - If lengths are in cm, area is in cm² - If lengths are in m, area is in m² - Always state the units in your answer **Common Triangle Types:** - Scalene: all sides different - Isosceles: two equal sides - Equilateral: all sides equal - Right-angled: one 90° angle **Exam Tips:** - Always identify the perpendicular height - it may not be a side of the triangle - Check your answer makes sense - area should be positive - Remember to halve the product of base and height