Question

In ΔDEF, d = 64 cm, e = 56 cm and f=83 cm. Find the area of ΔDEF to the nearest square centimeter.

Answer 1

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.