What is the simplified form of the area of a triangle with sides measuring 7, 8, and 9?

To find the area of a triangle with sides measuring 7, 8, and 9, we can use Heron's formula. Heron's formula states that the area of a triangle is given by:

Area = √[s(s-a)(s-b)(s-c)]

where ( s ) is the semi-perimeter of the triangle, calculated as:

( s = \frac{a+b+c}{2} )

In this case, ( a = 7 ), ( b = 8 ), and ( c = 9 ). First, we compute the semi-perimeter:

( s = \frac{7 + 8 + 9}{2} = \frac{24}{2} = 12 )

Next, we apply Heron's formula:

1. Calculate ( s-a ), ( s-b ), and ( s-c ):

• ( s - a = 12 - 7 = 5 )

• ( s - b = 12 - 8 = 4 )

• ( s - c = 12 - 9 = 3 )

2. Substitute these values into the formula:

Area = ( \sqrt{12 \cdot 5