Final answer:
Using Heron's formula, the area of a triangle with sides 56 cm, 60 cm, and 52 cm is calculated as approximately 751.32 cm², which does not match the provided answer choices. There might be a calculation error or the answer options are incorrect.
Step-by-step explanation:
To find the area of a triangle with sides 56 cm, 60 cm, and 52 cm, we can use Heron's formula which is suitable for any triangle, not just right triangles. First, we need to calculate the semi-perimeter (s) which is half the sum of the sides:
s = (56 cm + 60 cm + 52 cm) / 2 = 84 cm
Then we use Heron's formula for the area (A):
A = √[s(s - a)(s - b)(s - c)]
Where a, b, and c are the lengths of the sides of the triangle. Plugging in the side lengths we get:
A = √[84 cm * (84 cm - 56 cm) * (84 cm - 60 cm) * (84 cm - 52 cm)]
A = √[84 cm * 28 cm * 24 cm * 32 cm]
A = √[564480 cm²]
A = 751.32 cm² (rounded to two decimal places)
However, none of the provided answer options match the calculated area. There might have been a mistake in the calculations or in the provided answer options.