Question

Find the area of a triangle of sides 41 cm, 15 cm and 28 cm by using Heron's formula.
1. 112 cm²
2. 132 cm2
3. 126 cm2
4. 144 cm2

Answer 1

Correct Answer - Option 3 : 126 cm2

Given:

Three sides of the triangle are 41 cm, 15 cm and 28

Formula used:

The semi-perimeter of a triangle (s) = (a + b + c)/2

Area of triangle = √{s(s - a) (s - b) (s - c)}

where, a, b and c are sides of the triangle

Calculation:

The semi-perimeter of a triangle (s) = (41 + 15 + 28)/2

⇒ 84/2

⇒ 42 cm

Now, area of a triangle = √{42 × (42 - 41) × (42 - 15) × (42 - 28)}

⇒ √{42 × 1 × 27 × 14}

⇒ 14 × 9

⇒ 126 cm2

∴ The area of the triangle is 126 cm2.