1.

In triangle ABC, AD is prependicular to BC and DE is perpendicular to AB

Answer»

`{:(a,b,c,d),(p,r,Q,q):}`
`{:(a,b,c,d),(q,r,p,s):}`
`{:(a,b,c,d),(s,p,q,r):}`
`{:(a,b,c,d),(r,p,s,q):}`

Solution :
a. Area of `DeltaADB = (1)/(2) AD XX BD`
`= (1)/(2) c sin B xx c COS B`
`= (c^(2))/(4) sin 2B`
b. Area of `DeltaADC = (1)/(2) AD xx CD`
`= (1)/(2) b sin C xx b cos C = (b^(2))/(4) sin 2C`
c. Area of `DELTAADE = (1)/(2) AE xx DE`
`= (1)/(2) AD cos ((pi)/(2) - B) AD sin ((pi)/(2) - B)`
`= (1)/(4) AD^(2) sin 2B`
`= (1)/(4) c^(2) sin^(2) B sin 2B`
d. Area of `DeltaBDE = (1)/(2) BE xx DE`
`= (1)/(2) BD cos B xx AD sin ((pi)/(2) -B)`
`= (1)/(2) c cos B cos B xx c sin B cos B`
`= (1)/(4) c^(2) cos^(2) B sin 2B`


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