How do you find the area of a triangle?

To find the area of a triangle, use the formula: Area = 1/2 × base × height.

The area of a triangle can be calculated using the formula: Area = 1/2 × base × height. Here, the 'base' refers to the length of one side of the triangle, and the 'height' is the perpendicular distance from the base to the opposite vertex. This formula works for all types of triangles, whether they are scalene, isosceles, or equilateral.

For example, if you have a triangle with a base of 8 cm and a height of 5 cm, you would substitute these values into the formula to get: Area = 1/2 × 8 cm × 5 cm = 20 cm².

In cases where the height is not given, you might need to use other methods to find it. For right-angled triangles, the height is simply one of the two sides that form the right angle. For other triangles, you might need to use trigonometric ratios or the Pythagorean theorem to find the height.

Additionally, if you know the lengths of all three sides of the triangle, you can use Heron's formula to find the area. First, calculate the semi-perimeter (s) of the triangle: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides. Then, use the formula: Area = √[s(s - a)(s - b)(s - c)].

Understanding these methods will help you tackle a variety of problems involving the area of triangles in your GCSE Maths exams.