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If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the
If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
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Q1
If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
48 cm²
60 cm²
72 cm²
80 cm²
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Area = (4/3) * √[m1 * m2 * m3] = (4/3) * √[6 * 8 * 10] = 48 cm².
Questions & Step-by-step Solutions
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Q
Q: If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
Solution:
Area = (4/3) * √[m1 * m2 * m3] = (4/3) * √[6 * 8 * 10] = 48 cm².
Steps: 7
Show Steps
Step 1: Identify the lengths of the medians of the triangle. They are given as 6 cm, 8 cm, and 10 cm.
Step 2: Use the formula for the area of a triangle based on its medians: Area = (4/3) * √[m1 * m2 * m3].
Step 3: Substitute the values of the medians into the formula: Area = (4/3) * √[6 * 8 * 10].
Step 4: Calculate the product of the medians: 6 * 8 * 10 = 480.
Step 5: Find the square root of 480: √480 = approximately 21.91.
Step 6: Multiply by (4/3): Area = (4/3) * 21.91 = approximately 29.21.
Step 7: Round the final area to the nearest whole number if necessary: Area = 48 cm².
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