Question

Find the area of the triangle by Heron's formula.

• A. $12m^2$
• B. $24m^2$
• C. $40m^2$
• D. $6m^2$

Answer 1

The correct option is D $6m^2$

We use heron's formula to find the area of the triangle.

Let us find the semi perimeter:

$S=\frac{5+3+4}{2}=\frac{12}{2}=6$ cm

Now area of the triangle is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{6(6-5)(6-3)(6-4)}=\sqrt{6\times 1\times 3\times 2}=\sqrt{36}=6$ m${}^2$

Hence, the area of the triangle is $6$ m${}^2$.