Question

ABC is an equilateral triangle with sides measuring 4 unit semi circles are drawn as shown in the figure. AB &AC as diameter. Find the area of shaded portion

Answer 1

Answer:

Given AB=BC=AC

Area of Equilateral △ ABC = 17320.5cm  

2

 

                 ∴  

4

3

​  

 

​  

×AB  

2

 =17320.5

                    ∴ AB =200cm

Also, AB=2AD

∴     AD=100 cm =radius

Area of sector DAE + Area of sector DBF + Area of sector FCE

We know that area of sector =  

360

θ

​  

×π×r  

2

 

=3×  

360

60

​  

×3.14×100×100

=15700cm  

2

 

∴   Area of the shaded region = Area of equilateral triangle − Area of all sectors

                                         =17320.5−15700

                                         =1620.5cm  

2

 

solution

Step-by-step explanation: