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Question

In given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (Use π=22/7)
973843_8129b0620af148dc896fea005f80bf38.png

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Solution


In right AED, using Pythagoras theorem,

AD2=AE2+DE2=92+122=81+144=225cm

AD=225=15cm=diameter

Required area = ar. ABCD + ar. semi-circle - ar AED=(20×15)+12×227×(152)212×9×12

=300+88.392854=334.3928cm2

952917_973843_ans_a8e769c9b0544897b007489743a836f1.png

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