Learn to find the area of trapeziums and other irregular polygons by splitting them into familiar shapes.
A trapezium has one pair of parallel sides. Its area is found using: Area = ½ × (sum of parallel sides) × height, where height is the perpendicular distance between the parallel sides.
A trapezium has parallel sides 10cm and 6cm, with a height of 4cm. Find its area.
½ × (10+6) × 4 = ½ × 16 × 4 = 32 square cm
A trapezium has parallel sides 12cm and 8cm, with a height of 5cm. Find its area.
½ × (12+8) × 5 = ½ × 20 × 5 = 50 square cm
An irregular polygon can be split into triangles and trapeziums (or rectangles), and the total area found by adding up each piece's area separately.
A polygon is split into a triangle (area 20 sq cm) and a trapezium (area 35 sq cm). Find the total area.
20 + 35 = 55 square cm
An irregular pentagon is split into 3 triangles with areas 12, 18, and 15 square cm. Find its total area.
12 + 18 + 15 = 45 square cm
1. A trapezium has parallel sides 14cm and 10cm, with a height of 6cm. Find its area.
2. A trapezium has parallel sides 20cm and 12cm, with a height of 7cm. Find its area.
3. A trapezium has an area of 60 sq cm, parallel sides 15cm and 9cm. Find its height.
4. A polygon is split into a rectangle (area 40 sq cm) and a triangle (area 15 sq cm). Find its total area.
5. An irregular quadrilateral is split by a diagonal into two triangles with areas 24 and 18 square cm. Find its total area.