Question

A farmer wishes to find the area of a triangular piece of land by measurements it has a base of 120 rods and . Find the required area. 

Answer 1

The information given is not sufficient to calculate the area of the piece of land

But if the farmer measured the three sides of the triangular piece of land in Yards and got;

Side $1\to120yards$

Side $2\to330yards$

Side $3\to 420yards$

Area can be calculated using Hero's Formula where;

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

Where $S=\frac{1}{2}$ of the perimeter of the Triangular piece of land

And a,b,c are the measured sides

$S=\frac{120+330+420}{2}=435$

$A=\sqrt{435(435-120)(435-330)(435-420)}$

$=\sqrt{435×315×105×15}$

$=14,691$ square yards