Question

Find the area of triany ABC in which ab=7cm bc=5cm and ac=4cm

Answer 1

Area of the ∆ ABC = 9.8 cm^2

Step-by-step explanation:

Given :

A ∆ ABC, in which AB = c = 7cm, BC = a = 5 cm, AC = b = 4 cm.

To find :

The area of the ∆ ABC.

Solution :

Perimeter of the triangle ABC = 7 + 5 + 4 = 16 cm.

Semi-perimeter (s) = 8 cm.

Using Heron's formula for area of a ∆

Area =

$\sqrt{s(s - a)(s - b)(s - c)}$

=

$\sqrt{8(8 - 5)(8 - 4)(8 - 7)} \\ \implies \sqrt{8 \times 3 \times 4 \times 1} \\ \implies \sqrt{16 \times 6} \\ \implies4 \sqrt{6} \: \: {cm}^{2} \\ \implies \: 4 \times 2.45 \: {cm}^{2} \\ \implies \: 9.8 \: \: {cm}^{2}$

Hence, the area of the triangle = 4√6 cm^2

= 9.8 cm^2