GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Aug 2020, 12:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the area of quadrilateral ABCD shown above?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65764

### Show Tags

16 Jun 2020, 09:55
00:00

Difficulty:

(N/A)

Question Stats:

43% (01:33) correct 57% (03:10) wrong based on 14 sessions

### HideShow timer Statistics

What is the area of quadrilateral ABCD shown above?

A. 14
B. 16
C. 18
D. 20
E. 21

Are You Up For the Challenge: 700 Level Questions

Attachment:

2020-06-16_2151.png [ 37.75 KiB | Viewed 515 times ]

_________________
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 2049
Location: India

### Show Tags

16 Jun 2020, 11:42
5
Attachment:

Untitled.png [ 9.45 KiB | Viewed 448 times ]

Invert the triangle BCD about BD as shown in the above figure.

Area of quadrilateral ABCD is equivalent to Area of isosceles right angle triangle ABC(in the right)

Area of isosceles right angle triangle ABC $$= \frac{1}{2}* 6*6 =18$$
##### General Discussion
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

### Show Tags

20 Jun 2020, 13:16
Bunuel wrote:

What is the area of quadrilateral ABCD shown above?

A. 14
B. 16
C. 18
D. 20
E. 21

Are You Up For the Challenge: 700 Level Questions

Attachment:
The attachment 2020-06-16_2151.png is no longer available

Attachment:

triangle.png [ 20.37 KiB | Viewed 280 times ]

We are going to draw triangle CFD (see diagram above) such that angle F is a right angle and angle FCD = angle BCD = 45 degrees. We see that triangle CFD is a 45-45-90 right triangle. We will argue that the area of quadrilateral ABCD is equal to the area of triangle CFD. The argument is as follows:

Both quadrilateral ABCD and triangle CFD have the quadrilateral region CBED in common. Outside of this common region, quadrilateral ABCD has a triangular region AED and triangle CFD has a triangular region BEF. However, both triangles AED and BEF are congruent since angle F and angle A are congruent (they are right angles), angle AED and angle BEF are congruent (they are vertex angles) and side BE and side DE are congruent (they are the congruent sides of isosceles triangle BED). Therefore, triangles AED and BEF have the same area and if we add the quadrilateral region CBED to each of these triangles, we have quadrilateral ABCD and triangle CFD having the same area. So instead of finding the area of quadrilateral ABCD, we can just find the area of triangle CFD, which is easier since it’s an isosceles right triangle. Of course, we need to know one side of this triangle and we will make another argument that FD = 6 since it’s equal to AB. The argument is as follows:

We have mentioned above that BE = DE and since triangles AED and BEF are congruent, AE = FE. However, since AB = BE + AE and FD = FE + DE, AB = FD. Lastly, since AB = 6, FD = 6.

Since triangle CFD is an isosceles right triangle, its area is ½ x (FD)^2 = ½ x 6^2 = 18.

_________________

# Scott Woodbury-Stewart | Founder and CEO | Scott@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

What is the area of quadrilateral ABCD shown above?   [#permalink] 20 Jun 2020, 13:16