In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU

In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU

Answer Details

To find the area of the trapezium PQRU, we need to know the length of its height or perpendicular distance between the parallel sides PQ and RU. We can find this height by using the area of the parallelogram PQTU, which has the same base PQ and height as the trapezium, and a known area of 32 cm². Area of parallelogram PQTU = base × height 32 cm² = 4 cm × height Height = 8 cm Now we can use the formula for the area of a trapezium: Area of trapezium PQRU = (sum of parallel sides × height) ÷ 2 = (PQ + RU) × height ÷ 2 = (4 cm + 10 cm) × 8 cm ÷ 2 = 56 cm² Therefore, the area of trapezium PQRU is 56 cm². Answer option (B) is correct.