Question

8. If each side of an isosceles triangle is 3√2 and its base is 8 , then find the area of an isosceles
triangle

Answer 1

Answer:

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)}

s(s−a)(s−b)(s−c)

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

2

a+b+c

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

2

3

2

+3

2

+8

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)}

(3

2

+4)×(3

2

+4−3

2

)×(3

2

+4−3

2

)×(3

2

+4−8)

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

(3

2

+4)×(3

2

−4)×16

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

(18−16)×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

S=2

a+b+c

=

2

8+8+9

=12.5

By Heron's formula

Δ=

s(s−a)(s−b)(s−c)

=

(12.5)(3.5)(4.5)(4.5)

=29.765cm

2

.