A triangle has side lengths of 5 units, 6 units, and 7 units. Find its area.

To solve this problem, we can use Heron’s formula. Let’s denote the side lengths as a, b, and c.

a = 5 units , b = 6 units and c = 7 units

The area of triangle is given by

\$A = sqrt(s times (s - a) times (s - b) times (s - c))\$.

where s is the semi-perimeter of the triangle is given by

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

Substitute a = 5 ,b = 6 and c = 7 in semi-perimeter formula

\$s = (5 + 6 + 7) / 2 \$

After simplification

s= 9 units

Now Substitute the values in the area formula

\$A = sqrt(9 times (9 - 5) times (9 - 6) times (9 - 7))\$

After simplification

\$A = sqrt(9 times 4 times 3 times 2)\$

After simplification

\$A = sqrt(216)\$

After simplification

\$A = 14.7 units^2\$

Answer

The area of the triangle is \$14.7 units^2\$.