A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is its area?

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is its area?

Step 1: Identify the lengths of the sides of the triangle. They are 7 cm, 24 cm, and 25 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2, where a, b, and c are the lengths of the sides.
Step 3: Substitute the values into the formula: s = (7 + 24 + 25) / 2 = 28 cm.
Step 4: Use Heron's formula to find the area: Area = √(s(s-a)(s-b)(s-c).
Step 5: Calculate (s-a), (s-b), and (s-c): (28-7) = 21, (28-24) = 4, (28-25) = 3.
Step 6: Substitute these values into Heron's formula: Area = √(28 * 21 * 4 * 3).
Step 7: Calculate the product: 28 * 21 = 588, then 588 * 4 = 2352, and finally 2352 * 3 = 7056.
Step 8: Find the square root of 7056 to get the area: Area = √7056 = 84 cm².

Heron's Formula – A method for calculating the area of a triangle when the lengths of all three sides are known.
Semi-perimeter – The semi-perimeter (s) is half the sum of the triangle's side lengths, used in Heron's formula.
Triangle Inequality Theorem – A principle that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.