Question

the circular portion of the following figures are semicircles. for each find perimeter and area​

Answer 1

Answer:

first question apply Pythagoras theorem.

and for the 2nd one you can understand from fig

Answer 2

Answer:

b)  Perimeter  = 39.85 cm, Area = 89.28 cm²  

c)   Perimeter = 56.571 cm,  Area =  127.285 cm²        

Step-by-step explanation:

Given problem

Finding the perimeter and area of the given figures  

Given that circular portions of following figures are semicircles

(b) in this the figure is combination of right angled triangle and semicircle

here radius of the semi circle r = 5 cm  

⇒ diameter of semi circle d = 2r =2(5)  = 10 cm  

⇒ perimeter of the semicircle = πr ( without diameter)  

                                                 =  $\frac{22}{7} (5)$ = 15.71 cm

⇒ in the triangle hypotenuse = √200 cm = √2(10)² = 10√2 cm  

⇒ side of triangle = diameter of the semicircle

⇒  side of the triangle  = 10 cm

⇒  sides of the triangle are

√200 cm, 10 cm and 10 cm    [∵ two sides are equal in the triangle ]

⇒ perimeter of triangle = 10√2 + 10 + 10

                                     = 20 + 10√2    

                                    = 20 + 10(1.414)           (√2 value take as 1.414)

                                    = 20 + 14.14 = 34.14 cm

Perimeter of the figure  

= triangle perimeter+semicircle perimeter - length of common side of triangle and semicircle ( which is not belongs to perimeter)

=  34.14 cm + 15.71 cm - 10 cm  = 39.85 cm      

Area of the figure  

=   Area of the triangle  + area of semicircle

=      $\frac{1}{2} (base) (height)$   +    $\frac{\pi r^{2}}{2}$  

=           $\frac{1}{2} (10)(10)$        +     $\frac{\frac{22}{7}(25) }{2}$  

=           5 (10)       +    $\frac{11(25)}{7}$  

=         50  + 39.28  =  89.28 cm²  

(c) in this figure is combination of 2 small and 1 large semicircle  

⇒ Given that diameter of the large semicircle D = 18 cm

⇒ radius of the large semi circle R = 18/2 = 9 cm

⇒ diameter of the small semi circles d = 18/2  = 9 cm

⇒  radius of the small semicircle r = 9/2 = 4.5 cm

Perimeter of the figure

= perimeter of 2 small semicircles + perimeter of large semicircle

=  2( πr )  + πR             (without diameters)

=  π( 2r + R )  = π [ 2(4.5) + 9 ]

=  π (9 + 9) = 18 π  or 18 (22/7) = 56.571 cm      

Area of the figure  

= area of the 2 semi circles  + area of the large semicircle

= 2( π r²/2)  + π R²/2

=     π r²  + πR²/2

=   π ( r² + R²/2 )  = π[ (4.5)² + (9/2)² ]

= π [ (4.5)² + (4.5)²]   = π [ 20.25 + 20.25]

= π (40.5)   =   40.5 π  or  40.5(22/7) = 127.285 cm²