In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of

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Question: In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI?

Options:

Correct Answer: 96 cm²

Solution:

Using Heron\'s formula, s = (12 + 16 + 20) / 2 = 24 cm. Area = √(s(s-a)(s-b)(s-c)) = √(24(24-12)(24-16)(24-20)) = √(24*12*8*4) = 96 cm².

In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI?

In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI?

Step 1: Identify the lengths of the sides of triangle GHI. GH = 12 cm, HI = 16 cm, GI = 20 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 = (12 + 16 + 20) / 2.
Step 4: Add the lengths: 12 + 16 + 20 = 48.
Step 5: Divide by 2 to find s: s = 48 / 2 = 24 cm.
Step 6: Use Heron's formula to find the area: Area = √(s(s-a)(s-b)(s-c).
Step 7: Substitute the values into Heron's formula: Area = √(24(24-12)(24-16)(24-20)).
Step 8: Calculate each term: (24-12) = 12, (24-16) = 8, (24-20) = 4.
Step 9: Now substitute these values back into the formula: Area = √(24 * 12 * 8 * 4).
Step 10: Calculate the product: 24 * 12 = 288, then 288 * 8 = 2304, and finally 2304 * 4 = 9216.
Step 11: Find the square root of 9216 to get the area: Area = √9216 = 96 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 (s) is half the sum of the triangle's side lengths, used in Heron's formula.
Square Root Calculation – Understanding how to compute the square root of a product to find the area.