Question

Use Heron's formula to find the area of a triangle of lengths $7,8$ and $9$.

• A. $12\sqrt{5}$
• B. $11\sqrt{5}$
• C. $6\sqrt{5}$
• D. None of the above

Answer 1

The correct option is A $12\sqrt{5}$

We will find the area of triangle with lengths $7,8$ and $9$ using herons formula:

$S=\frac{7+8+9}{2}=\frac{24}{2}=12$ units

Now area is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{12(12-7)(12-8)(12-9)}=\sqrt{12\times 5\times 4\times 3}=\sqrt{720}=12\sqrt{5}$ sq.units

Hence, area of triangle is $12\sqrt{5}$sq.units.