Final answer:
Using Heron's formula and the given side lengths of a triangle (19m, 20m, 21m), the semi-perimeter is calculated as 30m and the area is approximately 172.47m², which corresponds to choice c. 172m².
Step-by-step explanation:
To determine the area of a triangle with sides of lengths a = 19m, b = 20m, and c = 21m, one useful method is Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides. The first step is to compute the semi-perimeter of the triangle, which is half the perimeter:
s = (a + b + c) / 2 = (19m + 20m + 21m) / 2 = 30m.
Then, Heron's formula gives the area (A) of the triangle:
A = √[s(s - a)(s - b)(s - c)],
where s is the semi-perimeter and a, b, c are the sides of the triangle.
Substitute the known values:
A = √[30m(30m - 19m)(30m - 20m)(30m - 21m)],
A = √[30m(11m)(10m)(9m)],
A = √[29700m²],
A ≈ 172.47m²,
So, the closest answer to the provided choices would be c. 172m².