Find the area of a trapezium whose parallel sides are 10 cm and 20 cm and non-parallel sides are equal to 10 cm.

Correct option is B

Given:
Length of parallel sides: a = 10 cm, b = 20 cm
Length of non-parallel sides: each = 10 cm
Formula Used:
Area of trapezium = $$\frac 12$$​ × (sum of parallel sides) × height
Solution:
When non-parallel sides are equal, a perpendicular from the top vertex to the base splits the trapezium into two right-angled triangles and a rectangle in between.
Let h be the height.
The difference between the bases is 10 cm, split equally on both sides
=> base of each right triangle = 5 cm.
h² + 5² = 10²
=> h = $$\sqrt{100 − 25} = \sqrt{75} = 5\sqrt 3$$​ cm
Area of trapezium =  $$\frac{1}{2} \times (10 + 20) \times 5\sqrt{3} = 15 \times 5\sqrt{3} = 75\sqrt{3}$$ sq. cm.​