Question

The base of isosceles triangle is 10cm and one of its equal sides is 13cm. Find the area using Herons 's formula. ​

Answer 1

Given:-

• Base of the triangle = 10 cm
• Equal sides of the triangle = 13 cm

To Find:-

• Find the area using Heron's formula

Solution:-

Sides of the triangle:-

a = 10 cm

b = 13 cm

c = 13 cm

To find area using Heron's formula we first need to find the semi-perimeter of the given sides of the triangle,

We know,

✭ s = (a + b + c)/2

Hence,

s = (10 + 13 + 13)/2

=> s = (10 + 26)/2

=> s = 36/2

=> s = 18

Now,

Applying Heron's formula,

We know,

✭ A = √s(s - a) (s - b) (s - c)

Hence,

A = √18(18 - 10) (18 - 13) (18 - 13)

=> A = √18 × 8 × 5 × 5

=> A = √2 × 3 × 3 × 2 × 2 × 2 × 5 × 5

=> A = 2 × 2 × 3 × 5

=> A = 60 cm²

Therefore the area of this isosceles triangle is 60 cm².

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