Question

Find the area of an isosceles triangle having the base 6 cm and the length of each side 5 cm
full solve​

Answer 1

Answer:

Area of the isosceles triangle = 12 cm²

Step-by-step explanation:

Given :

Base = 6 cm

Second side = 5 cm

Third side = 5 cm

To find :

The area of the isosceles triangle

Taken :

First find the semi-perimeter of the triangle . So , the formula to find the semi-perimeter use this formula -:

$\boxed{\sf{s=\dfrac{a+b+c}{2}}}$

Where,

s = Semi - perimeter

a = First side

b = Second side

c = Third side

After that to find the area of the triangle use this formula -:

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

Solution :

Semi - perimeter -:

$:\implies\sf{s=\dfrac{6cm+5cm+5cm}{2}}$

$:\implies\sf{s=\cancel{\dfrac{16cm}{2}}}$

$:\implies\sf{s=8cm}$

Area of the isosceles triangle -:

$:\implies\sf{A=\sqrt{8(8-6)(8-5)(8-5)}{cm}^{2}}$

$:\implies\sf{A=\sqrt{8\times2\times3\times3}{cm}^{2}}$

$:\implies\sf{A=\sqrt{(2\times4)\times2\times{3}^{2}}{cm}^{2}}$

$:\implies\sf{A=\sqrt{4\times{2}^{2}\times{3}^{2}}{cm}^{2}}$

$:\implies\sf{A=\sqrt{{2}^{2}\times{2}^{2}\times{3}^{2}}{cm}^{2}}$

$:\implies\sf{A=2\times2\times3\:\:\:{cm}^{2}}$

$:\implies\sf{A={12cm}^{2}}$

So , the area of the isosceles triangle is 12cm² .