Question

What is the ratio of area of outermost square to that of the shaded region, if each of the marked points are the midpoints of the line segments they are touching?​

Answer 1

Answer:

Let the center of circle be at O. AC is diagonal of square ABCD

AC=4

2

cm

we have AE=CF=1cm each

EF=AC−AE−CF

EF=42 −2

radius of circle =21

EF=21(42-2)=22 −1

Area of shaded region = area (ABCD) − (area of circle + 4× area of each quadrant)

=4×4−[π×(22 −1) 2 +4× 41 π(1) 2 ]

=16−π{(2 2 −1)2 +1}

=16−π{8+1−4 2 +1}

=16−(10−42 )π

=16−13.64439 (Taking 2

=1.414,π=3.14)

Area =2.36cm

2

hope it helps you ✅✅✅