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)

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- September 29th 2008, 04:09 PMfabxx[SOLVED] Find the area of rectangle ABCD
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) - September 29th 2008, 04:17 PMJhevon
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 - September 29th 2008, 04:37 PMSoroban
Hello, fabxx!

Did you make a sketch?

Quote:

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)

- September 29th 2008, 05:08 PMfabxx
- September 29th 2008, 05:21 PMJhevon