Question

in the given figure , ABCD is a parallelogram​

Answer 1

Step-by-step explanation:

Figure shows the parallelogram ABCD, line PQ dran parallel to BD , ΔABP and ΔADQ as given in the question.

let us draw line QR || BC and line SP || AB.

in ΔCDB, QP is parallel to DB; hence begin mathsize 12px style fraction numerator C Q over denominator C D end fraction space equals space fraction numerator C P over denominator C B end fraction end style ..................(1)

Above eqn.(1) can be written as,

begin mathsize 12px style 1 minus fraction numerator C Q over denominator C D end fraction space equals space 1 space minus space fraction numerator C P over denominator C B end fraction space space space space space o r space space space space fraction numerator C D minus C Q over denominator C D end fraction space equals space fraction numerator C B minus C P over denominator C B end fraction space space

h e n c e space fraction numerator D Q over denominator C D end fraction equals fraction numerator B P over denominator B C end fraction space equals space k end style

Let H and h are respective perpendicular height of parallelogram ARQD and ABPS

Area of paralleleogram ARQD = AR×H = AR×RQ×sinθ = DQ×BC×sinθ = k×CD×BC×sinθ .................(1)

Area of paralleleogram ABPS = AB×h = AB×BP×sinθ = AB×BP×sinθ = k×BC×AB×sinθ .................(2)

From (1) and (2), since AB = CD, Area of paralleleogram ARQD = Area of paralleleogram ABPS ....................(3)

Eqn.(3) is written as, 2×area of ΔADQ = 2×area of ΔABP

hence , area of ΔADQ = area of ΔABP

Answer 2

Answer: 10m

Step-by-step explanation:

Sides AD=20 = b

AB=16 = b'

height CE = h = 8

DF = h' =?

Since,

area of parallelogram

=1/2*b*h = 1/2*b'*h'

1/2*20*8 = 1/2*16*h'

80 = 8*h'

h'=10

DF = 10m