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?

If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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.

Medians of a Triangle – Medians are line segments that connect a vertex of a triangle to the midpoint of the opposite side, and their lengths can be used to calculate the area of the triangle.
Area Calculation – The area of a triangle can be calculated using the lengths of its medians with the formula Area = (4/3) * √[m1 * m2 * m3].
Geometric Properties – Understanding the relationship between the medians and the area of a triangle is crucial for solving problems related to triangle geometry.