The figure (ii) given below shows a field with the measurements given in metres. Find the area of the field.

From figure,

Area of right angled △AXB = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × BX × AX

= $\dfrac{1}{2}$ × 30 × 12

= 180 m².

Area of trapezium XZCB = $\dfrac{1}{2} \times$ (sum of parallel sides) × distance between them

= $\dfrac{1}{2}$ × (BX + CZ) × 15

= $\dfrac{1}{2}$ × (30 + 25) × 15

= $\dfrac{1}{2}$ × 55 × 15

= 412.5 cm².

Area of right angled △CZD = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × CZ × ZD

= $\dfrac{1}{2}$ × 25 × 10

= 125 m².

Area of △AED = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × AD × EY

= $\dfrac{1}{2}$ × 37 × 20

= 370 m².

Area of field = Area of right angled △AXB + Area of trapezium XZCB + Area of right angled △CZD + Area of △AED

= 180 + 412.5 + 125 + 370 = 1087.5 m².

Hence, area of field = 1087.5 m².