Final answer:
To find the area of a triangle, you need to use the formula 1/2 * base * height. In this case, the sides of the triangle are given, so you need to find the base and height using the semi-perimeter formula. Once you have the base and height, you can calculate the area using the formula.
Step-by-step explanation:
The formula for finding the area of a triangle is 1/2 * base * height. To find the area, multiply the base by the height and then divide the product by 2. In this question, the sides of the triangle are given as a = 44in, b = 66in, and c = 88in. However, the formula requires the base and height to calculate the area, not the sides.
To find the base and height, we can use the Heron's formula to calculate the semi-perimeter of the triangle. The formula is s = (a + b + c) / 2. Substituting the given values, we have s = (44 + 66 + 88) / 2 = 198 / 2 = 99.
Next, we can find the base and height using the semi-perimeter value. The formulas for the base and height are:
base = 2 * sqrt(s * (s - a) * (s - b) * (s - c)) / (b + c)
height = 2 * sqrt(s * (s - a) * (s - b) * (s - c)) / a
Substituting the values, we have:
base = 2 * sqrt(99 * (99 - 44) * (99 - 66) * (99 - 88)) / (66 + 88) ≈ 57.33in
height = 2 * sqrt(99 * (99 - 44) * (99 - 66) * (99 - 88)) / 44 ≈ 1.43in
Now, we can calculate the area using the formula:
Area = 1/2 * base * height ≈ 1/2 * 57.33 * 1.43 = 41.09in²