21) A

The third side of the ** equilateral triangle** is the diameter of the semi-circle.

Therefore, diameter of semi-circle = ‘x’ cm

Radius = ½x = (ˣ⁄₂)

We first need to find the area of the equilateral triangle. In order to do this, we need to find its height using Pythagoras theorem.

Divide the equilateral triangle into two right-angled triangles.

Hypotenuse = ‘x’

1st side = ½x

2nd side (height) = A

x² = (½x)² + A²

x² – ¼x² = A²

¾x² = A²

A = √(¾x²) = __x√3
__

*2*

Area of equilateral triangle = 2 x area of right-angled triangle

Area of 1 right-angled triangle = __ 1 __ * (__x√3)__ * __ x __ = __x²√3
__ 2 2 2 8

Area of equilateral triangle = 2 * __x²√3__ = __x²√3
__ 8 4

__Area of semi-circle = ½πr²__

__ 1 __ * π * __ x² __ = __πx²
__ 2 2² 8

Total area = area of triangle + area of semi-circle

__x²√3__ + __πx²
__ 4 8

__2x²√3 + πx²
__ 8

__2x²√3 + πx²
__ 8

**x² (2√3 + π)
**

**8**

So the answer is A