Question

In a triangle ABC , Ab=15cm,Bc=13cm and Ac = 14cm, the area of Triangle ABC is_____ (in cm^2)​

Answer 1

Step-by-step explanation:

In triangle ABC

Given sides

• AB=15cm
• BC=13cm
• AC=14cm

Let's use Herons formula

$\\\qquad\quad\sf {:}\longrightarrow Semiperimeter=s=\dfrac {a+b+c}{2}$

$\\\qquad\quad\sf {:}\longrightarrow S=\dfrac {15+13+14}{2}$

$\\\qquad\quad\sf {:}\longrightarrow S=\dfrac {42}{2}$

$\\\qquad\quad\sf {:}\longrightarrow S=21$

• Semiperimeter =s=21cm

According to Herons formula

$\boxed{\sf Area=\sqrt {s (s-a)(s-b)(s-c)}}$

$\\\qquad\quad\sf {:}\longrightarrow Area=\sqrt {(21 (21-15)(21-13)(21-14)}$

$\\\qquad\quad\sf {:}\longrightarrow Area=\sqrt{21(6\times 8\times 7)}$

$\\\qquad\quad\sf {:}\longrightarrow Area=\sqrt {21\times 336}$

$\\\qquad\quad\sf {:}\longrightarrow Area=\sqrt {7056}$

$\\\qquad\quad\sf {:}\longrightarrow Area=84cm^2$