Question

If each side of an isosceles triangle is 3 root 2 cm and its base is 8 cm then find the area of an isosceles triangle. ​with herons formula

Answer 1

Answer:

The Area of isosceles triangle using Heron's formula is 4√2  cm² .

Step-by-step explanation:

Given as :

For an isosceles triangle ABC

The measure of side AB = a = 3√2  cm

The measure of side AC = b = 3√2  cm

The measure of base side BC = c = 8 cm

Let The Area of isosceles triangle = A square cm

Applying Heron's formula

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

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

i.e s = $\dfrac{3\sqrt{2} +3\sqrt{2} + 8}{2}$

Or, s = 3√2 + 4

o, A = $\sqrt{(3\sqrt{2}+4)\times (3\sqrt{2}+4-3\sqrt{2})\times(3\sqrt{2}+4-3\sqrt{2})\times (3\sqrt{2}+4-8)}$

Or, A = $\sqrt{(3\sqrt{2}+4)\times (3\sqrt{2}-4)\times 16}$

or, A = $\sqrt{(18-16)\times 16}$

Or, A = √32

i.e A = 4√2  cm²

So, The Area of isosceles triangle = A = 4√2  cm²

Hence, The Area of isosceles triangle using Heron's formula is 4√2  cm² . Answer

Answer 2

I hope this will you satisfied.