Question

in the figure find the area of the shaded region​

Answer 1

Step-by-step explanation:

It is impossible to compute the area of an unshaded region with the given data as we do not know the formula of the area of that shape.

So to find the area of the unshaded region, we divide it into a square in the middle and 4 semi-circles around it, which looks like the figure below

From the figure if we observe the line segment from A to B = 14 cm.

AB = 3 + 3 + 2(diameter D of the circle)

     = 6 + 2(2r)

14 = 6 + 4r

Hence radius of the semi-circle (r) = 2cm.

Now, AB can also be written as AB = 3 + 3 + r + r + a (side of the inside square)

⟹14 = 6 + 2 + 2 + a

Therefore the side of the inner square = 4cm.

Now, the area of the whole big square whose side is 14cm is s2= (14)2=196cm2

Area of a small inside square whose side is 4cm is a2=42=16cm2

Area of 4 semi-circles is A = 4×πr22=4×3.14×222=25.12cm2

Now, area of shaded region = area of the big whole square – an area of the small inner square – an area of 4 semi-circles.

⟹Area of shaded region = 196 – 16 – 25.12 = 154.88cm2.

Note: To solve this type of question the key is to divide the unshaded region into known shapes and then we compute its area. We then subtract this from the total area to find the area of the unshaded part.

Area of square with side a = a2

Area of a semicircle with radius r =πr22.