A field is in the shape of a trapezium whose parallel sides are 200 m and 400 m long, whereas each of other two sides is 260 m long. What is the area (in m )of the field?

72000

We know that,

Area of trapezium = \(\frac{1}{2}\) × (Sum of parallel side) × (Distance between parallel side)

Given,

The parallel sides = 200 m and 400 m

The other two sides = 260 m

Here,

ABCD is a trapezium

AB = 200,CD = 400,

BC = AD = 260                                                                                          

AB = EF = 200 cm and DE = FC

CD = DE + EF + FC

400 = DE + 200 + DE

2DE = 400 – 200 = 200

DE = \(\frac{200}{2}\) = 100

In △BFC

BC² = BF² + FC²

(260)² = BF² + (100)²

BF² = 67600 – 10000 = 57600

BF = 240 cm

Area of trapezium = \(\frac{1}{2}\) × (400 + 200) × 240 = 120 × 600 = 72000 m²