1

Problem

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

2

Step

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

3

Formula

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))\$

4

Hint

Calculate the semi-perimeter(s)

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

1

Step

Substitute the values

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

s = 9 cm

2

Step

Therefore, s value is 9 cm.

3

Step

Substitute the values into Heron’s formula

\$A = \sqrt(9 \times (9 - 6) \times (9 - 8) \times (9 - 4))\$ \$A = \sqrt(9 \times (3) \times (1) \times (5))\$

4

Step

After Simplication

\$A = \sqrt((27)×(5))cm^2\$
⇒ \$A = \sqrt135cm^2\$

4

Solution

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

5

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

6

Choice-A

Incorrect, because \$\sqrt 132\$ is not equal to the calculated area \$\sqrt 135\$

Wrong \$\sqrt 132 cm^2\$

7

Choice-B

Incorrect, because \$\sqrt 134\$ is not equal to the calculated area \$\sqrt 135\$

Wrong \$\sqrt 134 cm^2\$

8

Choice-C

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

Correct \$\sqrt 135 cm^2\$

9

Choice-D

It is incorrect, because \$\sqrt 133\$ is not equal to the calculated area \$\sqrt 135\$

Wrong \$\sqrt 133 cm^2\$

10

Answer

Option

C

11

Sumup

Please summarize choices