Find the area of the scalene triangle ABC with the sides 8 cm, 6 cm and 4 cm.

The given base (b) = 8 cm, side (a) = 6cm, and c = 4 cm

Heron’s formula states that the area(A) of a triangle with sides a,b, and c is given by:

\$sqrt(s \times (s-a) \times (s-b) \times (s-c))\$

Calculate the semi-perimeter(s)

\$"s" = (a + b + c)/2\$

Substitute the values

\$"s" = (6 + 8 + 4)/2\$

\$"s" = (18cm)/2\$

\$"s" = 9cm\$

Therefore, s value is 9 cm.

Substitute the values into Heron’s formula

\$"A" = sqrt((9cm) \times (9-6)cm \times (9-8)cm \times (9-4)cm)\$

\$"A" = sqrt((9cm) \times (3cm) \times (1cm) \times (5cm))\$

After Simplication we get,

⇒ \$sqrt((27)\times(5)(cm)^2)\$

⇒ \$sqrt(135)(cm)^2\$

Therefore, the area of scalene triangle is \$sqrt(135)(cm)^2\$.

Can you summarize what you’ve understood in the above steps?

Choice A is incorrect, because \$\sqrt(132)\$ is not equal to the calculated area \$\sqrt(135)\$

\$sqrt(132)(cm)^2\$

Choice B is incorrect, because \$\sqrt(134)\$ is not equal to the calculated area \$\sqrt(135)\$

\$sqrt(134)(cm)^2\$

Choice C is correct, because \$\sqrt(135)\$ is equal to the calculated area using Heron’s formula for the given scalene triangle

\$sqrt(135)(cm)^2\$

Choice D is incorrect, because \$\sqrt(133)\$ is not equal to the calculated area \$\sqrt(135)\$

\$sqrt(133)(cm)^2\$

Option

C

Can you summarize what you’ve understood in the above steps?