Final answer:
The area of the triangle with sides 6cm, 4cm, and 5cm is approximately 9.9cm², calculated using Heron's formula and rounded to two significant figures.
Step-by-step explanation:
To work out the area of the triangle with sides 6cm, 4cm, and 5cm, you can use Heron's formula since the lengths of all three sides are given. Heron's formula states that the area of a triangle with sides of lengths a, b, and c is sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle (s = (a+b+c)/2).
First, calculate the semi-perimeter: s = (6cm + 4cm + 5cm) / 2 = 7.5cm. Next, apply Heron's formula: Area = sqrt(7.5cm * (7.5cm - 6cm) * (7.5cm - 4cm) * (7.5cm - 5cm)) = sqrt(7.5cm * 1.5cm * 3.5cm * 2.5cm) = sqrt(98.4375cm²) = 9.92156742cm². When rounded to two significant figures, the result is 9.9cm².
The area of the triangle in question is, therefore, approximately 9.9cm².