Final answer:
In this case, the area of ΔDEF is approximately 1080.4 square centimeters.
Step-by-step explanation:
To find the area of a triangle (ΔDEF), we can use Heron's formula which states:
Area = √(s(s-a)(s-b)(s-c))
where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle.
So, in this case, we have:
- a = 64 cm
- b = 56 cm
- c = 83 cm
First, let's calculate the semi-perimeter:
s = (a + b + c) / 2
s = (64 + 56 + 83) / 2
s = 203 / 2
s = 101.5 cm
Now, we substitute the values into the formula:
Area = √(101.5(101.5-64)(101.5-56)(101.5-83))
Area ≈ √(101.5 * 37.5 * 45.5 * 18.5)
Area ≈ √(1166411.875)
Area ≈ 1080.4 cm²
Therefore, the area of ΔDEF is approximately 1080.4 square centimeters.