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Triangle KLM has KL=29,KM=28, and LM=22. What is the area of the triangle?

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Final answer:

The area of triangle KLM can be calculated using Heron's formula and when using the given side lengths, it is approximately 275.7 square units, to three significant figures.

Step-by-step explanation:

To find the area of triangle KLM, you can use Heron's formula, which allows you to find the area of a triangle when you know all three sides. Heron's formula is:

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the sides. First, calculate the semi-perimeter:

s = (KL + KM + LM) / 2

s = (29 + 28 + 22) / 2

s = 79 / 2

s = 39.5

Now, you can plug this along with the side lengths into Heron's formula:

Area = √[39.5(39.5 - 29)(39.5 - 28)(39.5 - 22)]

Area = √[39.5(10.5)(11.5)(17.5)]

Area = √[76012.8125]

Area ≈ 275.7 square units (rounded to three significant figures because side lengths are given to two decimal places or less)

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