Final answer:
To find the area of a triangle with side lengths of 7 cm, 8 cm, and 9 cm, we use Heron's formula with the semi-perimeter of the triangle. After calculating the semi-perimeter to be 12 cm, we find the area to be approximately 26.83 cm² when rounded to two decimal places.
Step-by-step explanation:
The area of a triangle with sides measuring 7 cm, 8 cm, and 9 cm cannot be directly found using the base and height formula since the height is not directly given. In this case, the Heron's formula is the appropriate tool for finding the area. Heron's formula states that the area (A) of a triangle with sides of lengths a, b, and c, and semi-perimeter (s) is given by:
A = √(s(s-a)(s-b)(s-c))
Firstly, calculate the semi-perimeter:
s = (a + b + c) / 2
s = (7 cm + 8 cm + 9 cm) / 2 = 12 cm
Now, apply the Heron's formula:
A = √(12 cm * (12 cm - 7 cm) * (12 cm - 8 cm) * (12 cm - 9 cm))
A = √(12 cm * 5 cm * 4 cm * 3 cm)
A = √(720 cm²)
A = 26.8328 cm²
Therefore, the area of the triangle is approximately 26.83 square centimeters when rounded to two decimal places, to match the significant figures in the measurements provided.