Answer :
Final answer:
The area of the triangle with sides 7.5 cm, 18 cm, and 19.5 cm is calculated using Heron's formula. The semi-perimeter of the triangle is first calculated, and then substituted along with the side lengths into the formula, giving an area of approximately 63.75 cm².
Explanation:
To find the area of a triangle when the lengths of the three sides are known, we can use Heron's formula. This formula states that the area of a triangle is equal to the square root of the product of the semi-perimeter (s) and the difference between the semi-perimeter and each side of the triangle. In this case, the lengths of the sides are a = 7.5 cm, b = 18 cm, and c = 19.5 cm.
First, we calculate the semi-perimeter of the triangle with the formula s = (a + b + c) / 2. So, s = (7.5 cm + 18 cm + 19.5 cm) / 2 = 22.5 cm.
Next, we substitute the semi-perimeter and the lengths of the sides into Heron's formula: Area = √[s(s - a)(s - b)(s - c)]; Area = √[22.5 cm (22.5 cm - 7.5 cm)(22.5 cm - 18 cm)(22.5 cm - 19.5 cm)]
By calculating the above equation you should find the area to be approximately 63.75 cm², so the correct answer is a) 63.75 cm².
Learn more about Heron's Formula here:
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