Question

In the given figure, the breadth of the rectangle
is 10 cm. Two semicircles are drawn such that
the breadth of the rectangle becomes their
diameter. If the area of the shaded region is
100 cm?, what would be the shortest distance
(in cm) between the semicircles?
10 cm​

Answer 1

The area of given figure is 1085 cm².                  

To find : Area of the given figure.

Given : Rectangle and semi-circle.    

Rectangle :

Sides : Length = 10 cm

          Breadth = 30 cm

Area of rectangle = Length × Breadth

                            = 10 × 30

Area of rectangle = 300 cm².    

Semi-circle :

Area of semi-circle = πr²

From the figure,

Remaining parts are semi-circle.

Note : Figure is attached below

There are four semi-circles.    

Finding area for 2 semi-circles :

Radius (  ) = Length of the rectangle = 10 cm

Radius (  ) =  = 5 cm

= 5 cm.

Area of semi-circle =  =  =  =  = 39.25 cm²

Area of 2 semi-circle = 2 × 39.25 = 78.5 cm².

Finding area of another 2 semi-circles :

Radius (  ) = Breadth of the rectangle = 30 cm

Radius (  ) =  = 15 cm

= 15 cm.

Area of semi-circle =  =  =  =  = 353.25 cm²

Area of another 2 semi-circles = 2 × 353.25 = 706.5 cm²

Area of 4 semi-circle = Area of 2 semi-circle + Area of another 2 semicircle.

                                  = 78.5 + 706.5

                                  = 785 cm²

So, area of 4 semi-circle is 392.5 cm².

Area of given figure = Area of rectangle + Area of 4 semi-circle

                                =  300 + 785

                                = 1085 cm².

Therefore, the area of given figure is 1085 cm².

Answer 2

Answer:

55/7

Step-by-step explanation:

The diameter of the semicircle is 10 units.

The diameter of the semicircle is 10 units.There are 2 equal semicircle which means they will make a circle. The area of the circle is 25 pie. The area of the shaded part is 100 so, 25pie+100 is the area of whole rectangle. To find the length we have to divide the number

The diameter of the semicircle is 10 units.There are 2 equal semicircle which means they will make a circle. The area of the circle is 25 pie. The area of the shaded part is 100 so, 25pie+100 is the area of whole rectangle. To find the length we have to divide the number by 10 because the breadth is 10. But firstly multiply25/1*22/7+100/1 which is 1250/7. Now divide it by 10 , 1250/7/10/1. The length is 125/7. Now to find the shortest distance add the two radius and subtract 10 from 125/7 which is equal to 55/7 or 11+2pie