The area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².
The area of a triangle can be computed by the formula √{s(s - a)(s - b)(s - c)}, where a, b, and c, are the three sides of the triangle, and s is the semi-perimeter of the triangle, that is, s = (a + b + c)/2.
In the question, we are asked to find the area of the triangle, whose sides are 51cm, 37cm, and 30cm.
Thus, we take a = 51cm, b = 37cm, and c = 30cm.
The perimeter of the triangle = a + b + c = 51cm + 37cm + 30cm = 118cm.
Hence, the semi-perimeter of the triangle, s = (a + b + c)/2 = 118cm/2 = 59cm.
Hence, using the formula for the area of the triangle:
√{s(s - a)(s - b)(s - c)}
= √{59(59 - 51)(59 - 37)(59 - 30)} cm²
= √{59 * 8 * 18 * 29} cm²
= √246384 cm²
= 496.37 cm².
Thus, the area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².
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