Question

. The square below has sides of length 3 cm
and the arcs have centres at the corners.
Find the shaded area.

Answer 1

Step-by-step explanation:

Attach the diagram for better understanding of the question

Answer 2

Answer:

The shaded area can be divided into two equal circular segments by drawing the diagonal of the square. The area of a segment is the area of a quarter circle with radius 3 cm minus the area of the right triangle whose legs are 3 cm each:

Asegment=Aquarter−Atriangle

A

segment

=A

quarter

−A

triangle

Asegment=14πr2−12bh

A

segment

=

4

1

πr

2

−

2

1

bh

Asegment=14π(3)2−12(3)(3)

A

segment

=

4

1

π(3)

2

−

2

1

(3)(3)

Asegment=94π−92

A

segment

=

4

9

π−

2

9

So, the shaded area is:

Ashaded=2Asegment

A

shaded

=2A

segment

Ashaded=2(94π−92)

A

shaded

=2(

4

9

π−

2

9

)

Ashaded=92π−9≈5.14 cm2

A

shaded

=

2

9

π−9≈5.14 cm

2