Find the area of a triangle, whose sides are 6 cm, 0.08 m and 4 cm

Correct option is C

Given:

Side 1 = 6 cm

Side 2 = 0.08 m = 8 cm (converted to cm)

Side 3 = 4 cm

Formula Used:

To find the area of a triangle with three sides, we can use Heron's formula. The formula is:

A = $$\sqrt{s(s-a)(s-b)(s-c)}$$​​

Where:

a, b, c are the lengths of the sides of the triangle

s is the semi-perimeter, calculated as:

s = $$\frac{a + b + c}{2}$$

​Solution:

the semi-perimeter s:

s = $$\frac{6 + 8 + 4}{2} = \frac{18}{2} = 9 \text{ cm}$$​​

Substituting into Heron's formula:

A = $$\sqrt{9(9 - 6)(9 - 8)(9 - 4)}$$​​

=$$\sqrt{9 \times 3 \times 1 \times 5}$$​​

​$$= \sqrt{135}$$​​

​$$= 3\sqrt{15}\, \text{cm}^2$$​​

Thus, the area of the triangle is approximately $$3\sqrt{15}$$​ cm².