# Form a rectangular region ABCD , a right triangle AED with AE= 9 cm and DE = 12cm is cut off. On other end taking BC as diameter , a semi - circle is added on the region. Find the area of the shaded region. (Use pi= 3.14)

Complete question  : Form a rectangular region ABCD with AB  =  20 cm , a right triangle AED with AE= 9 cm and DE = 12cm is cut off. On other end taking BC as diameter , a semi - circle is added on the region. Find the area of the shaded region. (Use pi= 3.14) ,

Solution :  As ABCD is a rectangular region , SO AB  =  CD and BC  =  AD

And our diagram from given information is , As :

Now we Apply Pythagoras theorem in $∆$ AED , and get

So,

BC  =  15 cm   ( As we know AD  =  BC )

So,

And
We know Area of triangle  = , So
Area of $∆$ AED =
And Area of rectangle  =  Length $×$ Breadth , So
Area of rectangular part ABCD  = 20 $×$ 15  =  300 cm2
And
We know Area of semicircle  = , So
Area of semicircle  =
So,
Area of shaded region  =  Area of rectangular part  + Area of semicircle  -  Area of $∆$ AED
Area of shaded region  = 300 + 88.3125  - 54  =  334.3125 cm2                                                ( Ans )

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