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