Find the area of a triangular field, the length of . . .

Question : Find the area of a triangular field, the length of whose sides are 275 m, 660 m and 715 m. What is the cost of cultivating the field at the rate of Rs 200 per hectare? [1 hectare = 10000 m²]

Doubt by Aastha

Solution : 

Here
a=275 m

b=660 m

c=715 m

s = (a+b+c)/2
s = (275+660+715)/2
s = 1650/2
s = 825 m

Using Heron's Formula
Area of triangular field
= √[s(s-a)(s-b)(s-c)]
= √[825(825-275)(825-660)(825-715)]
= √[825×550×165×110]
= √[3×5×5×11×2×5×5×11×3×5×11×2×5×11]
= √[2×2×3×3×5×5×5×5×5×5×11×11×11×11]
= 2×3×5×5×5×11×11
= 30×25×121
= 750×121
= 90750 m²

= (90750/10000) Hectares

= 9.075 Hectares

Cost of cultivating 1 Hectares of field = Rs 200
Cost of cultivating 9.075 Hectares of field = Rs(200×9.075)
= Rs 1815