the area of the triangle with sides of lengths 13 cm, 6 cm, and 9 cm is approximately 23.66 square centimeters.
To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. Heron's formula states that the area (A) of a triangle with sides of lengths a, b, and c can be calculated using the following formula:
A = √[s(s - a)(s - b)(s - c)]
Where:
s is the semiperimeter (half of the perimeter), given by s = (a + b + c) / 2.
a, b, and c are the lengths of the triangle's sides.
In your case, the lengths of the three sides are a = 13 cm, b = 6 cm, and c = 9 cm. Now, calculate the semiperimeter (s):
s = (a + b + c) / 2
s = (13 + 6 + 9) / 2
s = 14 cm
Now, use Heron's formula to find the area (A):
A = √[14(14 - 13)(14 - 6)(14 - 9)]
A = √[14(1)(8)(5)]
A = √[560]
A ≈ 23.66 cm² (rounded to two decimal places)
So, the area of the triangle with sides of lengths 13 cm, 6 cm, and 9 cm is approximately 23.66 square centimeters.
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