**What is the Heron’s formula**

**Heron’s formula: **If we have all sides of triangle and their is no way to find height then we use this formula for area of triangle.

**Heron’s Formula Example Problems With Solutions**

**Example 1: **For given figure find the s (s – a).

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**Example 2: **If semiperimeter of a triangle is 60 cm & its two sides are 45 cm, 40 cm then find third side.

**Solution:**

**Example 3: **If perimeter of an equilateral triangle is 96 cm, then find its each side.

**Solution:**

**Example 4: **If one side from two equal sides of a Δ is 14 cm and semiperimeter is 22.5 cm then find the third side.

**Solution:**

**Example 5: **Find the length of AD in given figure, if EC = 4 cm and AB = 5 cm.

**Solution:**

**Example 6: **Find the area of a triangle whose sides are of lengths 52 cm, 56 cm and 60 cm respectively.

**Solution:**

**Example 7: **Using Heron’s formula, find the area of an equilateral triangle of side a units.

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**Example 8: **Find the area of an isosceles triangle each of whose equal sides is 13 cm and whose base is 24 cm.

**Solution:**

**Example 9: **The perimeter of a triangular field is 450 m and its sides are in the ratio 13 : 12 : 5. Find the area of the triangle.

**Solution:**

**Example 10: **Find the percentage increase in the area of a triangle if its each side is doubled.

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**Example 11: **The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find (i) the area of the triangle and (ii) the height corresponding to the longest side.

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**Example 12: **Find the area of the shaded region in figure:

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**Example 13: **Find the area of an isosceles triangle of its sides are a cm, a cm and b cm.

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**Example 14: **A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board ?

**Solution:**