In parellelogram ABCD, DE is perpendicular to BC and AD = 24

Question

(a)  If AB= 2x + 4 and CD = x + 7, then CD =

 

(b)  If the lengths of EC and BE are in the ratio 1:3 then EC =

 

(c)   The length of ED is

 

(d)   The area of ABD is ------- square units

 

(e)   The area of trapezoid ABED is ......... square units 

Answer 1

It is important to draw a sketch. When you do you will see that AB=CD

Therefore: 2x+4=x+7 which immediately gives you x=3 so that AB=CD=10

AD=BC=24 (look at your sketch)

The ratio of 1/3 means that there are 4 parts in the whole of which EC is one and BE is 3,i.e.

    EC=1/4 of 24=6 and BE = 3/4 of 24=18  (notice that 6/18=1/3!)

Triangle DEC is a right triangle with hypotenuse 10 and one leg 6; the other leg, namely ED must be 8

   (if you do not recognize this as a 3-4-5 right triangle, use the Law of Pythagoras to get the 8.)

The area of triangle ABD: again look at your sketch...the base is AD=24 and because the figure is a parallelogram the 

   altitude is ED=8 and the area is 24*8/2=96.

The area of the trapezoid is half the sum of the 2 bases * the altitude=(18+24)*8/2=168.