Question

The sides of a triangle are $56cm$, $60cm$ and $52cm$ long. Then the area of the triangle is

• A. $1322c{m}^2$
• B. $1311c{m}^2$
• C. $1344c{m}^2$
• D. $1392c{m}^2$

Answer 1

The correct option is C

$1344c{m}^2$

Explanation for the correct option:

Find the area of the triangle

Let the sides of the triangle be $a=56cm,b=60cm,c=52cm$

To find the area of the triangle, we will use Heron's formula.

Heron's formula can be given that: $A=\sqrt{s(s-a)(s-b)(s-c)}$

Where $s=\frac{a+b+c}{2}$ and $a,b,c$ are the sides of the triangle.

Now, the semi-perimeter will be,

$$\begin{gathered} s=\frac{56+60+52}{2} \\ \Rightarrow s=\frac{168}{2} \\ \Rightarrow s=84cm \end{gathered}$$

Now, the area of the triangle will be,

$$\begin{gathered} A=\sqrt{84(84-56)(84-60)(84-52)} \\ \Rightarrow A=\sqrt{84\left(28\right)\left(24\right)\left(32\right)} \\ \Rightarrow A=1344c{m}^2 \end{gathered}$$

Hence, the correct option is (c)$1344c{m}^2$.