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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 using Heron\'s formula?

Options:

  1. 96 cm²
  2. 96√3 cm²
  3. 48 cm²
  4. 64 cm²

Correct Answer: 96 cm²

Solution: 

First, calculate the semi-perimeter s = (12 + 16 + 20) / 2 = 24 cm. Then, 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

Practice Questions

Q1
In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI using Heron's formula?
  1. 96 cm²
  2. 96√3 cm²
  3. 48 cm²
  4. 64 cm²

Questions & Step-by-Step Solutions

In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI using Heron's formula?
  • 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. Here, s = (12 + 16 + 20) / 2.
  • Step 3: Perform the addition: 12 + 16 + 20 = 48.
  • Step 4: Divide the sum by 2 to find the semi-perimeter: s = 48 / 2 = 24 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: Substitute the values into the formula: area = √[24(24-12)(24-16)(24-20)].
  • Step 7: Calculate each term inside the square root: (24-12) = 12, (24-16) = 8, (24-20) = 4.
  • Step 8: Now substitute these values back into the formula: area = √[24 * 12 * 8 * 4].
  • Step 9: Calculate the product: 24 * 12 = 288, then 288 * 8 = 2304, and finally 2304 * 4 = 9216.
  • Step 10: Take the square root of 9216 to find 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 is half the sum of the lengths of the sides of the triangle, used in Heron's formula.
  • Square Root Calculation – Understanding how to compute the square root of a product in the context of area calculation.
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