Question

Find the area if an isosceles triangle whose equal sides are of length 15 cm each and third side is 12 cm long *​

Answer 1

Solution

Given:-

• Equal side are of length of isosceles triangle = 15 cm
• Third triangle = 12 cm

Find:-

• Area of isosceles triangle

Explanation

Using Formula

☛ Area of isosceles triangle = 1/2.[ Base * Height ]

In Diagram , isosceles ∆ABC

where,

• AB = AC = 15 cm
• BC = 12 cm

First calculate Height of triangle .

For this, first take a perpendicular line " AD" of "BC"

So, BD = DC = 12/2 = 6 cm

Now, take right ∆ABD

By, Pythagoras theorem

$\boxed{\underline{\tt{\red{\:(Hypotenuse)^2\:=\:(Base)^2+(Perpendicular)^2}}}}$

Where,

• Hypotenuse = AB = 15 cm
• Base = BD = 6 cm
• Perpendicular = AD = ?

So, keep above values

==> ( 15)² = (6)² + AD²

==> AD² = 225 - 36

==> AD² = 189

==>AD = √189

==>AD = 3√21 cm. [Height ]

So, Now calculate Area of isosceles ∆ABC

==> Area of isosceles triangle = 1/2.[ 12 * 3√21]

==> Area of isosceles triangle = 6 * 3√21

==> Area of isosceles triangle = 18√21 cm²

Hence

• Area of isosceles triangle = 18√21cm²