Area of combination of figures

Let’s take a rectangle

And add a semicircle on top of side CD & AB

What will be the area of total figure?

Area of total figure = Area of rectangle + Area of top semicircle + Area of bottom semicircle.

So, area gets added

Let’s take some values & actually solve it

What will be the area of the figure given below?

Here,

Area of total Figure =  Area of rectangle  + Area of top semicircle + Area of bottom semicircle

Here, Both semicircle will have the same diameter,

So, their area will be the same

∴ Area of total figure = Area of rectangle + 2 × Area of semicircle

Let’s find them out separately

Area of rectangle

Length = l = AB

      = 20 cm

Breadth = b = BC

      = 5 cm

Area of rectangle ABCD = l × b

     = AB × BC

     = 20 × 5

     = 100 cm ²

Area of semi-circle

Diameter = 20 cm

   Radius = r = Diameter/2

        = 20/2

= 10 cm

Now,

  Area of semi-circle = (Area of circle)/2

  = πr ² /2

  = (3.14  (10) ² )/2

  = (314 × 100)/(100 × 2)

  = 314/2

  = 157 cm ²

Now,

  Area of figure = Area of rectangle ABCD + 2 Area of semi-circle

 = 100 + 2 × (157)

 = 100 + 314

 = 414 cm ²

∴ Area of given figure is 514 cm ²