Final answer:
The area of a triangle with sides 8 cm, 11 cm, and 13 cm can be found using Heron's formula. By calculating the semi-perimeter and plugging in the values into the formula, we determine the area is 8√{30} cm², which corresponds to answer choice (a).
Step-by-step explanation:
To find the area of a triangle with sides of lengths 8 cm, 11 cm, and 13 cm, you can use Heron's formula since the triangle is not necessarily a right-angled triangle. First, calculate the semi-perimeter s by adding the lengths of the sides and dividing by 2:
s = (8 + 11 + 13) / 2 = 16 cm
Now, apply Heron's formula to find the area (A):
A = √[s(s - 8)(s - 11)(s - 13)]
Plugging in the values, we get:
A = √[16(16 - 8)(16 - 11)(16 - 13)]
Which simplifies to:
A = √[16(8)(5)(3)]
And further simplifies to:
A = √[1920]
Calculating the square root, you find that the area of the triangle is:
A = 8√{30} cm²
Therefore, the correct answer is (a) 8√{30}cm².