Perimeter of a trapezoid.. 3:)
Consider that isosceles trapezoid. The Segments, BF and CE are all perpendicular to the longer base. The ratio of segments, AF:AD = 1:4 . The perimeter of Triangle ABF is 24 cm. The Perimeter of Rectangle, BCEF is 40 cm. The Perimeter of Trapezoid ABCE is 48 cm.
Question:
What is the perimeter of Trapezoid ABCD ?
Take note: Pls. give your solution if you get the answer.
The answer is 56.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let x/4 = Segment AF = ED and x = AD
The segment, FE = x - (x/2) = x/2
Let y = Segments BF and CE
the Triangle ABF has sides, AF = x/4 , BF = y, and AB = 24-(x/4 + y)
Therefore, the trapezoid ABCE ha sides, BC = x/2 , CE = y , AE = x/4 + x/2 , and AB = 24-(x/4 + y)
Then, the perimeter of trapezium ABCE is:
x/2 + y + x/4 + x/2 + 24 - (x/4 + y) = 48
x + 24 = 48
x = 24
and
the rectangle BCEF has a perimeter, 40 cm. Therefore,
x/2 + y = 40/2
24/2 + y = 40/2
y = 8
Then,
BC = x/2 = 24/2 = 12
CD = AB = 24 - (x/4 + y) = 24 - (6+8) = 10
AD = 24
Therefore, the perimeter of Trapezoid ABCD is: 12 + 10 + 10 + 24 = 56 cm.