Question

Find the area of triangle ABC in which AB is 7cm, BC is 5 cm and AC is 4 cm

Answer 1

$4 \sqrt{6}$

Answer 2

✬ Area = 4√6 cm² ✬

Step-by-step explanation:

Given:

• In a ∆ABC.
• Length of AB is 7 cm.
• Length of BC is 5 cm.
• Length of AC is 4 cm.

To Find:

• What is the area of ∆ABC ?

Solution: We have to find the area of given triangle by using Pythagoras Theorem.

First find the Semi-Perimeter (S) of ∆ABC

➼ S = Sum of all sides/2

➼ S = AB + BC + AC/2

➼ S = 7 + 5 + 4/2 = 16/2 = 8

As we know that

★ Heron's Formula = √s( s – a )( s – b )( s – c ) ★

$\implies{\rm }$ Area = √8(8 – 7)(8 – 5)(8 – 4)

$\implies{\rm }$ √8 $\times$ 1 $\times$ 3 $\times$ 4

$\implies{\rm }$ √2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 2 $\times$ 2

$\implies{\rm }$ 2 $\times$ 2 √2 $\times$ 3

$\implies{\rm }$ 4√6 cm²

Hence, the area of ∆ABC is 4√6 cm².