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The three sides of a triangle are 9 cm, 11 cm and 14 cm. Find the area of the triangle?
1. 12√17
2. 6√17
3. 15√17
4. 14√17

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Correct Answer - Option 1 : 12√17

Given:

Sides of triangle;

S1 = 9 cm

S2 = 11 cm

S3 = 14 cm

Formula used:

Using Heron's formula;

Area of a scalene triangle = √[s(s - a)(s - b)(s - c)]

Where 's' is the semi perimeter of the triangle.

Calculation:

Semi-perimeter of the triangle = (S1 + S2 + S3)/2

⇒ (9 + 11 + 14)/2

⇒ 17 cm

Area of triangle = √[17(17 - 9)(17 - 11)(17 - 14)] cm2 

⇒ √[17 × (8) × (6) × (3)] cm2 

⇒ 12√17 cm2 

∴ The area of triangle is 12√17 cm2

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