Question

If the lengths of the three sides of a trapezium other than the base are 10 cm each, then the maximum area of the trapezium is:

• A. 100 cm²
• B. \(25√ 3 cm^2\)
• C. \(75√ 3 cm^2\)
• D. \(100√ 3 cm^2\)

Answer 1

The Correct Option is C

Since three sides of the trapezium are equal to 10 cm, we consider the configuration
where these sides form two equilateral triangles at the ends.
Area of one equilateral triangle with side 10 cm:
\(A = \frac{√ 3} {4} × (10)^2 = 25√ 3 cm^2\)
Since there are three such triangles, the total area is:
Total Area = \(3 × 25√3 = 75√3 cm^2\)