Answer:

The area of a circle is 20.41 units.

Step-by-step explanation:

Formula

Area of a circle = pi r^{2}

Where r is the radius of a circle.

As given

First take when the radius of a circle is 2 unit.

pi = 3.14

radius = 2 units

Put in the formula

Area of a circle = 3.14times 2times 2

                                    = 12.56 unit

Second take when the radius of a circle is 3 unit.

pi = 3.14

radius = 3 units

Put in the formula

Area of a circle = 3.14times 3times 3

                                    = 28.26 unit

As given

The area of a circle whose area equals the half of the sum of the areas of two circles with radii 2 and 3.

Area of a circle = frac{Area of circle with radius 2units+Area of circle with radius 3units }{2}

Put the value in the  above

Area of a circle = frac{12.56 +28.26}{2}

Area of a circle = frac{40.82}{2}

Area of a circle = 20.41 units

Therefore the area of a circle is 20.41 units.