A field is in the shape of a trapezium, whose parallel sides measure 250 m and 110 m and non-parallel sides measure 150 m and 130 m. What is the area (in hectares) of the field?

Correct option is A

Given:

Parallel sides of trapezium = 250 m and 110 m

Non-parallel sides = 150 m and 130 m

Formula Used:

Semi perimeter of triangle = $$\frac{a+b+c}{2}$$​​

Area of triangle = $$\sqrt{s(s-a)(s-b)(s-c)}$$

​​Area of triangle = $$\frac{1}{2} \times \text{Base} \times \text{Height}$$​​

Area of trapezium = $$\frac{1}{2} \times (\text{sum of parallel sides}) \times$$​ height

1 hectare = 10,000 square meters

Solution:

Semi perimeter of triangle (S) = $$\frac{130 + 150 + 140}{2}$$ = 210 m

Area of triangle = $$\sqrt{210(210 - 130) (210 - 150) (210 -140)}$$ 

= $$\sqrt{210(80) (60) (70)}$$​​

= $$\sqrt{3 \times 70 \times 16 \times 5 \times 70 \times 12 \times 5}$$

= 70 $$\times$$ 4 $$\times$$ 5 $$\times$$ 6

= 8400 m² 

Now, By Area of triangle formula:  

8400 = $$\frac{1}{2} \times 140 \times \text{Height}$$

Height  = $$\frac{8400 \times 2}{140}$$

= 120 m

Now,

Area of trapezium = $$\frac{1}{2} \times (110 + 250) \times 120$$​​

= $$\frac{1}{2} \times (360) \times 120$$

= 21600 m²​

Convert to hectares:
= $$\frac{21600}{10000} = 2.16$$ hectares

Thus, the correct option is (a) 2.16 hectares
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