Areas of triangles, parallelograms and trapeziums together

First find the base and its height. The height is at right angles to the base. A slanting side's length is not the height. A parallelogram's area = base × height. A triangle's area is half of a parallelogram with the same base and height: base × height ÷ 2. A trapezium's area = (top + bottom) × height ÷ 2. A triangle with base 8 cm and height 5 cm: 8 × 5 = 40, 40 ÷ 2 = 20, so 20 cm². Quicker: halve the even number first to keep the numbers small: 8 ÷ 2 = 4, 4 × 5 = 20. A trapezium with top 3 cm, bottom 7 cm and height 4 cm: 3 + 7 = 10, 10 × 4 = 40, 40 ÷ 2 = 20 cm². Cutting the shapes up and rearranging them into rectangles or parallelograms shows where these formulas come from.