Question

Find the area of isosceles triangle whose equal sides are 6 cm , 6cm and 8 cm​

Answer 1

Step-by-step explanation:

wo equal sides of an isosceles triangle are 6cm each.

Third side of the triangle is 8cm.

To Find :

Area of the isosceles triangle.

Solution :

a = 6cm.

b = 6cm.

c = 8cm.

Now ,

So , The Area of the isosceles triangle is 8√5cm²..

Option a) 8√5cm² is correct..

Answer 2

Answer:

Area of the triangle = 8√5 cm²

Step-by-step explanation:

Given,

The sides of an isosceles triangle are 6cm,6cm, and 8cm

To find,

The area of the isosceles triangle

Recall the concepts:

The median and altitude of an isosceles triangle are the same line segments.

By Pythagoras theorem,

in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Area of the triangle = $\frac{1}{2}$ × base ×height ----------------(A)

Solution:

Let ABC be the isosceles triangle, AB and AC are equal sides.

AB= 6cm, AC = 6cm, BC = 8cm

AD is the line drawn from the vertex from A to BC. Then AD is the altitude and median of the triangle of ΔABC

AD⊥BC and BD = CD = 4cm

Then, we have ΔADB is a right-angled triangle.

By Pythagoras theorem,

AD² = AB² - BD²

AD² = 6² - 4²

AD² = 36 -16 =20

AD = $\sqrt{20}$ = 2√5cm

Height of the isosceles triangle = 2√5cm

Base  = 8cm

Substituting these values in equation(A)

Area of the triangle = $\frac{1}{2}$ × 2√5 × 8

= 8√5 cm²

Area of the triangle = 8√5 cm²

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