Question

Plz answer this

For 45 points​

Answer 1

       

Answer: 2.28r²

       

Draw diameters AB, BC, CD and DA as shown in the figure.

As the circles are congruent, the diameters are equal, so that ABCD is a square.

Consider square ABCD only. We're going to find the area of the shaded region according to this square.

Four semicircles with each sides of the square as diameters are included in the square.

As example, when we add the areas of the semicircles with AB and CD as diameters, and then subtract it from the area of the square, we get double the area of one such unshaded region in the square. There are four congruent unshaded regions.

When we subtract the double of this area thus obtained, we get the area of the shaded region.

Okay, let's start.

Let each side of the square , AB = BC = CD = DA, which are also diameters of the congruent circles, be 2r. r is the radius of the circles.

So, area of the square = (2r)² = 4r²

Area of a circle = πr²

Difference of areas of both the square and the circle = 4r² - πr² = (4 - π) r²

[Area of the square is greater than that of the circle. ]

This is area of two among the four congruent unshaded regions in the square.

Double this.

2 (4 - π) r²  =  2r²(4 - π)

Okay. Subtract this from the area of the square.

4r² - 2r²(4 - π)

⇒ 2r² (2 - (4 - π))

⇒ 2r² (2 - 4 + π)

⇒ 2r² (π - 2)

This is the area of the shaded region.

Let's take π as 3.14.

⇒ 2r² (3.14 - 2)

⇒ 2r² × 1.14

⇒ 2.28r²

So we get the answer.

Hope this helps. Plz mark it as the brainliest.

Thank you. :-))

           

Answer 2

here is your answer in the attachment given above