Math, asked by gautham94976, 6 hours ago

Smitha Shaded a square cardboard of side 23 cm , as shown below.

Attachments:

Answers

Answered by 72HurricanE
12

Answer:

a.) 364.52 cm²

Step-by-step explanation:

  • In the above question we have to find the area of the Shaded region.

  • So, if we will find the area of the Rectangle and then the area of the circle and subtract them.

  • Then, we will get the correct Answer.

Area of the Rectangle: Length x Breadth

Length = 23 cm

Breadth = 23 cm

Area = 23 x 23

529 cm²

Now, Area of the unshaded region:

  • The unshaded region contains four Semi - Circle.
  • 2 Semi - Circle is = 1 Circle
  • 4 Semi - Circle is = 2 Circle

Area of 2 circles will be: πr²

Radius = 7cm

Value of π = 22/7

Area = 22/7 x 7²

22 / 7 x 7 x 7

22 x 7

154 cm²

Now, Area of Unshaded region:

Area of Rectangle - Area of Circle

⇒529 - 154

375 cm²

364.52 cm² Approx

Answered by shownmintu
0

Answer:

The option A) 364.52~cm^2 is closest to the area of shaded region.

Tip:

  • Area of square =a^2 , where a is the side of the square.
  • Area of semicircle =\frac{\pi r^2}{2} , where r is the radius.

Explanation:

  • In this question we have given a square in which a figure is made off.
  • We have to find the area of shaded region.
  • We will find this by first finding the area of square and then subtract the area of unshaded region which was made by four semicircles and one square.

Step

Step 1 of 3:

The area of square whose sides are 23~cm:

=(23)^2

=529

Step 2 of 3:

Now, the area of unshaded region:

Area of four semicircles - Area of square

For radius and side of square :

23-3.5-3.5=16

So, radius of semicircle is 4~cm and side of square is 8~cm.

So, Area =4(\frac{\pi (4)^2}{2})+8\times8

              =4(8\pi )+64\\=100.57+64\\=164.57

Step 3 of 3:

Area of shaded region = Area of square -Area of unshaded region

                                      =529-164.57\\=364.43~~cm^2

Similar questions