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)