Question

what will be the area of given figure if ABCD is a rectangle with sides length 10 centimetre and braedth 30 cm and the other parts are all semicircles. ​

Answer 1

1085. 71 cm^2 will be the area of given figure if ABCD is a rectangle with sides length 10 centimetre and braedth 30 cm and the other parts are all semicircles. ​

• Area of given figure = Area of rectangle + Area of semicircles
• = l * b + 2 * π r^2/2 + 2 * π r^2/2
• as, there are a total of 4 semicircles,
• but 2 are of same radius and other 2 are of same radius
• considering length of rectangle as radius of 2 semicircles, we have, r = 10/2 = 5 cm
• considering length of rectangle as radius of 2 semicircles, we have, r = 30/2 = 15 cm
• = 10 * 30 + 2 * π 5^2/2 + 2 * π 15^2/2
• = 300 + 2 * π/2 (5^2+15^2)
• = 300 + π (25 + 225)
• = 300 + 22/7 (250)
• = 300 + 785.7
• = 1085. 71 cm^2      

Answer 2

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 ( $r_1$ ) = Length of the rectangle = 10 cm

Radius ( $r_1$ ) = $\frac{10}{2}$ = 5 cm

$r_1$ = 5 cm.

Area of semi-circle = $\frac{\pi(r_1)^2 }{2}$ = $\frac{\pi }{2} \times5\times5$ = $\frac{25\times3.14}{2}$ = $\frac{78.5}{2}$ = 39.25 cm²

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

Finding area of another 2 semi-circles :

Radius ( $r_2$ ) = Breadth of the rectangle = 30 cm

Radius ( $r_2$ ) = $\frac{30}{2}$ = 15 cm

$r_2$ = 15 cm.

Area of semi-circle = $\frac{\pi(r_2)^2 }{2}$ = $\frac{\pi }{2} \times15\times15$ = $\frac{225\times3.14}{2}$ = $\frac{706.5}{2}$ = 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.

To learn more...

1. In the given figure, ABCD is a rectangle of 20 cm * 10 cm. A semicircle is drawn with centre O . The radius is 10 root 2cm and it passes through A and B .Find the area of the shaded region

brainly.in/question/7138313

2. In fig. ABCD is a rectangle with AB= 14 cm and BC= 7 cm. Taking DC, BCand AD as diameter, three semicircles are drawn. Find the area of the shaded portion.

brainly.in/question/2975773