Hi, this is on the SAT OG Book page 747 #16
In rectangle ABCD, point E is the midpoint of line segment BC. If the area of quadrilateral ABED is , what is the area of the rectangle ABCD?
a)
b)
c)
d) 1
e)
note that the area of rectangle ABCD is given by AD*AB
now, ABED is a trapezium, thus its area is given by half the sum of the two parallel sides times the distance between them. that is (1/2)(BE + AD)*AB, and this is 2/3, so
(1/2)(BE + AD)*AB = 2/3
=> (BE + AD)*AB = 4/3
but, BE = (1/2)AD (this should be pretty obvious from a diagram if you drew or were given one), so that
=> (3/2)AD*AB = 4/3
=> AD*AB = 8/9
Hello, fabxx!
Did you make a sketch?
In rectangle ABCD, point E is the midpoint of line segment BC.
If the area of is , what is the area of ?
Code:D *---------------* C | * | | * | | * | F * - - - - - - - * E | | | | | | A *---------------* B
Draw median EF.
. . Hence: .
We are told that: .
We have: . . . . answer (c)