Question

Find the area of a triangle using Heron's formula

• A. $170c{m}^2$
• B. $160c{m}^2$
• C. $180c{m}^2$
• D. $200c{m}^2$

Answer 1

Answer: (C)

$180c{m}^2$

We find the area of triangle using herons formula:

$S=\frac{9+40+41}{2}=\frac{90}{2}=45$ cm

Now area is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{45(45-9)(45-40)(45-41)}=\sqrt{45\times 36\times 5\times 4}=\sqrt{32400}=180$ cm${}^2$

Hence, area of triangle is $180$ cm${}^2$.