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Question

A farmer has a triangular field with sides 240 m and 360 m, where he grew wheat. In another triangular field with sides 240 m, 320 m and 400 m adjacent to the previous field, he wanted to grow potatoes and onions. He divided the field into two parts by joining the mid point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions ?
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Solution

According to heron's formula A=p(pa)(pb)(pc)
p=a+b+c2
Area of the triangle with wheat=A1
p1=360+200+2402=400
A1=400(400200)(400240)(400360)=400(200)(160)(40)=22627.417m2=2.26Hectares
Similarly, Area of triangle 2 is A2
p2=320+400+2402=480
A2=480(480240)(480320)(480400)=480(240)(160)(80)=38400m2=3.84Hectares
Half of it is for onions=1.62Hectares, Other half is for potatoes=1.62Hectares



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