Question

In the given figure, ABCD is a rectangle in which AB = 60 and BC = 40 cm . If P, Q, R and S be the mid - points of AD, DC, CB and BA, find the area of the shaded region.​

Answer 1

Answer:

Here are two for the price of one (using Euler's formula):

cos(A+B)+isin(A+B)≡ei(A+B)≡eiA×eiB

≡[cos(A)+isin(A)][cos(B)+isin(B)]

≡[cos(A)cos(B)−sin(A)sin(B)]+i[sin(A)cos(B)+cos(A)sin(B)]

Now equate imaginary parts to give the result for sin(A+B) (and, if you want, equate real parts to give the result for cos(A+B)).

Answer 2

In the given figure, ABCD is a rectangle in which AB = 60 and BC = 40 cm . If P, Q, R and S be the mid - points of AD, DC, CB and BA, find the area of the shaded region.