Question

THE SIDES OF A TRIANGLE ARE 3M ,5M,6M FIND THE AREA OF THE TRIANGLE
ANSWER FAST ​

Answer 1

Answer:

Area of ∆ is √56 m²

Solution:

It is given that -

• a = 3 m
• b = 5 m
• c = 6 m

Now, we've to find the area of triangle.

Firstly we've to find the semi perimeter of traingle:

S = (a + b + c)/2

→ S = (3 + 5 + 6)/2

→ S = 14/2

→ S = 7 m

Using heron's formula:

Ar ∆ABC = √[s(s - a)(s - b)(s - c)]

→ Ar ∆ABC = √[7(7-3)(7-5)(7-6)]

→ Ar ∆ABC = √[7 × 4 × 2 × 1]

→ Ar ∆ABC = √56 m²

Hence, area of ∆ABC is √56 m²

Answer 2

Given :

• The sides of a triangle are 3 m, 5 m and 6 m.

To find :

• The area of the triangle =?

Step-by-step explanation :

Now, the formula to find the semi-perimeter of a triangle is :-

$\bigstar {\boxed {\bf S = \dfrac{ a+ b+ c}{2}}}$

Substituting value in above formula, we get

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\begin{lgathered}\begin{lgathered} \tt S = \dfrac{ 3 + 5 + 6 }{2}\\ \\ \tt =\dfrac{14}{2}\\ \\ \tt= 14 \div 2\\ \\ \tt= 7 \: m\end{lgathered}\end{lgathered}\end{lgathered}\end{lgathered}\end{lgathered}$

Now, by Heron's formula find the area of the triangular plot :

$\bigstar{\boxed{\bf Area \:of \triangle = {\sqrt{s(s-a) (s-b) (s-c)}}}}$

Substituting value in the above formula, we get,

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\begin{lgathered}{\tt = {\sqrt{7(7-3) (7-5)(7-6)}}} \\ \\ \tt = {\sqrt{7 \times 4\times 2 \times 1}} \\ \\ \tt = {\sqrt{7 \times 2 \times2 \times 2 \times 1}} \\ \\ \tt = {\sqrt{56}} \end{lgathered}\end{lgathered}\end{lgathered}\end{lgathered}$

Therefore, , The Area of the triangle = $\tt {\sqrt{56}}\: m^2$