Question

Find the area of the triangle with sides 13, 14 and 15 cm.
1. 84 cm²
2. 78 cm²
3. 66 cm²
4. 92 cm²

Answer 1

Correct Answer - Option 1 : 84 cm²

Given

Three sides of a triangle 13, 14 and 15 cm

Concept used

Area = \(\sqrt {s × \left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \)

Where s = semi perimeter

s = (a + b + c) / 2

Calculation

Here three sides:

a = 13 cm 

b = 14 cm 

c = 15 cm 

S = \(\dfrac{{13 + 14 + 15}}{2}\)

S = 21 cm

Area = \(\sqrt {21 × \left( {21 - 13} \right)\left( {21 - 14} \right)\left( {21 - 15} \right)} \)

Area = \(\sqrt {21\left( 8 \right)\left( 7 \right)\left( 6 \right)} \)

Area = \(\sqrt {21 × 21 × 16} \)

Area = 21 × 4 

Area = 84 cm²