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A parallelogram ABCD has perimeter equal to  124 . Let E be the foot of the perpendicular from A to BC, and let F be the foot of the perpendicular from A to CD. If AE= 7 and AF=24, what is the area of the parallelogram?

 Jan 3, 2021
 #1
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Perimeter  =  124

 

2(BC + CD)  = 124

 

BC + CD  =  62

 

CD  =  62 - BC

 

Area  of Paralleogram   = Area of Parallelogram

 

BC ( AE)  =  AF ( CD)

 

BC ( 7)  =  24 ( 62  - BC)

 

7BC  = 1488  - 24BC

 

31 BC =  1488

 

BC  = 1488/31  =  48

 

So....the area =  BC * 7 =  48 * 7   =   336 units^2

 

 

cool cool cool

 Jan 3, 2021
 #2
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P = 124           P/2 = 62            ∠B = ∠D  => x

 

7 / x + 24 / x = 62         x = 1/2     (this is sine of angles B and D)

 

AB = 1/2 * 7 = 14               AD = 1/2 * 24 = 48

 

Area             [ABCD] = 48 * 7 = 336     or      14 * 24 = 336

 Jan 4, 2021

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