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?
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
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
