Find the area of a triangle whose sides are 12 m, 14 m and 16 m.

Correct option is A

Given:

- Sides of the triangle: a = 12 m, b = 14 m, c = 16 m.

Formula Used:

Use Heron's formula to calculate the area.

Heron's formula states that the area of a triangle is:
Area = $$\sqrt{s(s-a)(s-b)(s-c)}$$​​
where ( s ) is the semi-perimeter of the triangle, given by:
​$$s = \frac{a + b + c}{2}$$​​

Solution:

Substitute the values of  ( a, b, c ):
​$$s = \frac{12 + 14 + 16}{2} = \frac{42}{2} = 21 \, \text{m}$$​​

Using Heron's formula:
Area  = $$\sqrt{21(21-12)(21-14)(21-16)}$$​​
Area  = $$\sqrt{21 \times 9 \times 7 \times 5}$$​​
Area  = $$21\sqrt{15}$$​​
Answer: The area of the triangle is approximately $$21\sqrt{15}$$​ m².