A triangle has sides of length 5 cm, 7 cm and 10 cm. Find the area of the triangle (in $$cm^2$$).​

Correct option is A

Given:
a = 5 cm
b = 7 cm
c = 10 cm
Formula Used:​
Perimeter = a + b + c
Semi-perimeter = S = $$\frac {a + b + c}{2}$$

$$\text{Area of Heron's formula} = \sqrt{s(s-a)(s-b)(s-c)}$$ 

Solution:

Perimeter = 5 + 7 + 10 = 22 cm

Semi-perimeter = s =$$\frac{22}2$$​ = 11 cm

Area of Heron's formula = $$\sqrt{s(s-a)(s-b)(s-c)}$$

$$\text{Area of Heron's formula} = \sqrt{11(11-5)(11-7)(11-10)} \\= \sqrt{11 \times 6 \times 4 \times 1} \\= 2\sqrt{66} \, \text{cm}^2$$​​​