Question

Plot the points $(2,3)(6,3)and(4,7)$ in a graphsheet.join them to make it a triangle find the area of the triangle

Answer 1

$a=\sqrt{(6-2{)}^2+0}=4$

$b=\sqrt{(3-7{)}^2+(6-4{)}^2}$

$=2\sqrt{5}$

$c=\sqrt{(7-3{)}^2+(4-2{)}^2}$

$=\sqrt{16+4}=2\sqrt{5}$

$\frac{a+b+c}{2}=s=\frac{4+2\sqrt{5}+2\sqrt{5}}{2}=2+2\sqrt{5}$

$A=\sqrt{(2+2\sqrt{5})(2+2\sqrt{5}-4)(2+2\sqrt{5}-2\sqrt{5})(2+2\sqrt{5}-2\sqrt{5})}$

$=\sqrt{(2+2\sqrt{5})(2\sqrt{5}-2)\times 2\times 2}$

$=\sqrt{(20-4)\times 2\times 2}=\sqrt{4^2\times 2^2}$

Area$=8$ sq. units.