Question

Use Heron's formula to find the area of a triangle of lengths $5cm,9cm$ and $12cm$.

• A. $\sqrt{26}c{m}^2$
• B. $2\sqrt{26}c{m}^2$
• C. $3\sqrt{26}c{m}^2$
• D. $4\sqrt{26}c{m}^2$

Answer 1

The correct option is D $4\sqrt{26}c{m}^2$

We will find the area of triangle with lengths $5$ cm, $9$ cm and $12$ cm using heron's formula:

$S=\frac{5+9+12}{2}=\frac{26}{2}=13$ units

Now area is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{13(13-5)(13-9)(13-12)}=\sqrt{13\times 8\times 4\times 1}=\sqrt{416}=4\sqrt{26}$ sq.units

Hence, area of triangle is $4\sqrt{26}c{m}^2$