In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of

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Question: In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)

Options:

Correct Answer: 120 cm²

Exam Year: 2019

Solution:

Using Heron\'s formula, semi-perimeter s = (10 + 24 + 26) / 2 = 30. Area = √(s(s-a)(s-b)(s-c)) = √(30*20*6*4) = 120 cm².

In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)

In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)

Step 1: Identify the lengths of the sides of triangle GHI. GH = 10 cm, HI = 24 cm, GI = 26 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. Here, s = (10 + 24 + 26) / 2.
Step 3: Perform the addition: 10 + 24 + 26 = 60.
Step 4: Divide the total by 2 to find the semi-perimeter: s = 60 / 2 = 30 cm.
Step 5: Use Heron's formula to find the area of the triangle. The formula is Area = √(s(s-a)(s-b)(s-c).
Step 6: Calculate (s - a), (s - b), and (s - c): (30 - 10) = 20, (30 - 24) = 6, (30 - 26) = 4.
Step 7: Substitute the values into Heron's formula: Area = √(30 * 20 * 6 * 4).
Step 8: Calculate the product inside the square root: 30 * 20 = 600, then 600 * 6 = 3600, and finally 3600 * 4 = 14400.
Step 9: Find the square root of 14400 to get the area: √14400 = 120 cm².

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Semi-perimeter – The semi-perimeter of a triangle is half the sum of its side lengths, used in Heron's formula.