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

 It is currently 22 Feb 2020, 05:31 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the area of the figure above?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61385
What is the area of the figure above?  [#permalink]

### Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 64% (01:56) correct 36% (01:59) wrong based on 72 sessions

### HideShow timer Statistics What is the area of the figure above?

A. $$40\sqrt{2}$$
B. 64
C. 68
D. 81
E. 92

Attachment: image2264.jpg [ 3.38 KiB | Viewed 1161 times ]

_________________
Director  P
Joined: 04 Sep 2015
Posts: 675
Location: India
WE: Information Technology (Computer Software)
Re: What is the area of the figure above?  [#permalink]

### Show Tags

1
What is the area:

A. 402√402
B. 64
C. 68
D. 81
E. 92

draw line parallel from both ends and to the opposite side,

then we have a square at the top and two rectangles of dimentions 2*8

so the triangle we are left with 8,8 ,x this will form a 45-45-90 trianlge and rule x,x,xroot2

or we can also say that the area of the triangle =32

then the area of the two rectangles=2*8*2=32

and the square at the top=2*2=4

so total area=32+32+4=68

Option C is correct.
Attachments triangle.jpg [ 9.75 KiB | Viewed 1026 times ]

SVP  D
Joined: 03 Jun 2019
Posts: 2013
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: What is the area of the figure above?  [#permalink]

### Show Tags

1
What is the area of the figure above?

A. 40√2
B. 64
C. 68
D. 81
E. 92

If we divide the figure as
A triangle of area = 8*8/2 = 32
A rectangle with area = 10*2 = 20
A rectangle with area = 8*2 = 16

Adding 3 areas = 32 + 20 + 16 = 68

IMO C
Manager  G
Joined: 08 Jan 2018
Posts: 148
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: What is the area of the figure above?  [#permalink]

### Show Tags

IMO-C

Refer attached Image.
Draw a line joining the vertices B & E

This divides the figure into an isosceles triangle & a trapezium.

From fig, Sides of parallel side of trapezium are 10 sqrt2 & (10 sqrt2 -2 sqrt2 ) and distance between them sqrt2

Area= 1/2 x (10 x 10) + 1/2 x (10 sqrt2 + 8sqrt2 ) x sqrt2 = 68
Attachments WhatsApp Image 2019-08-21 at 9.29.01 PM.jpeg [ 76.63 KiB | Viewed 1000 times ]

Originally posted by MayankSingh on 21 Aug 2019, 08:04.
Last edited by MayankSingh on 21 Aug 2019, 08:11, edited 1 time in total.
Senior Manager  P
Joined: 31 May 2018
Posts: 473
Location: United States
Concentration: Finance, Marketing
Re: What is the area of the figure above?  [#permalink]

### Show Tags

area of the given figure = area of a triangle ABE + area of a trapezium BCDE
= $$\frac{1}{2}$$*10*10 + $$\frac{1}{2}$$(10√2 +8√2 )√2

= 50 + 18
= 68
Attachments ps.png [ 7.88 KiB | Viewed 1009 times ]

GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5896
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the area of the figure above?  [#permalink]

### Show Tags

Image
What is the area of the figure above?

A. 402‾√402
B. 64
C. 68
D. 81
E. 92

divide the figure we get 2 rectangles; 10*2 + 8*2 ; 36
and an isosceles ∆ 8:8:8√2 ; area ; 1/2 * 8*8 ; 32
total area ; 36+ 32 ; 68
IMO C
Manager  P
Joined: 15 Jun 2019
Posts: 221
Re: What is the area of the figure above?  [#permalink]

### Show Tags

its area of square - area of right angled isoceles triangle of non hypotenuse side of 8

=10 ^2- 1/2 *8*8

=100- 32
=68
Senior Manager  P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 381
GPA: 4
Re: What is the area of the figure above?  [#permalink]

### Show Tags

This is how I did. Hope it helps.

Posted from my mobile device
Attachments IMG_20190821_223035.jpg [ 2.83 MiB | Viewed 940 times ]

Director  P
Joined: 25 Jul 2018
Posts: 562
Re: What is the area of the figure above?  [#permalink]

### Show Tags

2

We can continue the small sides (the length of the side =2) to get the square( the length of the side of square =10.

The area of the square =10*10=100

—> See the picture below.

Triangle ABC is right-angled isosceles triangle.
—> the area of ABC =(8*8)/2=32

—> the area of the figure = 100–32=68

Posted from my mobile device
Attachments FDAB4625-FA4B-4D52-B481-160642219A45.jpeg [ 869.06 KiB | Viewed 915 times ]

Director  D
Joined: 07 Mar 2019
Posts: 706
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: What is the area of the figure above?  [#permalink]

### Show Tags

What is the area of the figure above?

A. 402√402
B. 64
C. 68
D. 81
E. 92

Refer attached snapshot.

Alternative method is slightly longer.

Attachments

File comment: What is the area of the figure above What is the area of the figure above.jpg [ 1.08 MiB | Viewed 874 times ]

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Tutor S
Joined: 16 Sep 2014
Posts: 396
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Re: What is the area of the figure above?  [#permalink]

### Show Tags

See the image attached below,

We can complete a square since we have 3 angles of 90 degrees, and two sides that are equal. Then we can see the area is a square with length of 10, minus an isosceles right triangle with a side of 8. The triangle is isosceles because both sides are 8. The added outer angle must be 90 because a 4 sided polynomial must have all interior angles adding up to 360.
Therefore the area is 10*10 - 8*8/2 = 100 - 32 = 68.

Attachments completed image.png [ 35.47 KiB | Viewed 834 times ]

_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Intern  B
Joined: 24 Jul 2019
Posts: 2
Re: What is the area of the figure above?  [#permalink]

### Show Tags

Area of the figure = Area of the triangle formed by extending the sides with value 10 and 10 to form one big isosceles triangle - area of 2 small isosceles triangle which have one side as 2.

side of the smaller triangle: one side will be 2 and the hypotenuse = 2*sqrt2

Area of the smaller triangle = (1/2)*2*2 = 2

Side of bigger triangle: Base and height = 10+2=12, 12 and hypotenuse = 12*sqrt2
Area of the bigger triangle = (1/2)*12*12 = 72

Area of the figure = 72 - 2*2 = 68
CR Forum Moderator P
Joined: 18 May 2019
Posts: 709
Re: What is the area of the figure above?  [#permalink]

### Show Tags

From the image below, triangle ABE is a right angled isosceles triangle. This means that EB=(10^2 + 10^2)^0.5 = 200^0.5 = 10(2)^0.5
Area of solid ABCDE = Area of Triangle ABE + Area of trapezoid EBCD.
Area of triangle ABE = (10*10)/2 = 50.

Angle AED (90) = angle AEB + angle DEF ....(1)
Since we know that triangle ABE is a right angled isosceles triangle, angle AEB = angle ABE = 45. Hence angle DEF=45, implying triangle EFD is a right angled isosceles triangle. This also means that EF=FD=(2)^0.5
Likewise GB=CG=(2)^0.5
Hence DC = EB-EF-GB = 8(2)^0.5
So, Area of EBCD=
{(10(2)^0.5 + 8(2)^0.5)*(2)^0.5}/2 ={(18)(2)/2}
=18
So Area of ABCDE = 50 + 18 = 68

Posted from my mobile device
Attachments image.jpg [ 1.58 MiB | Viewed 776 times ]

VP  P
Joined: 24 Nov 2016
Posts: 1224
Location: United States
Re: What is the area of the figure above?  [#permalink]

### Show Tags

Quote:
What is the area of the figure above?

A. 40√2
B. 64
C. 68
D. 81
E. 92

shaded: area of square - area of triangle = 10*10 - (8*8/2) = 68
VP  D
Joined: 18 Dec 2017
Posts: 1118
Location: United States (KS)
GMAT 1: 600 Q46 V27 Re: What is the area of the figure above?  [#permalink]

### Show Tags

Just think of it as a square of 10*10 having area as 100.
A right triangle whose 2 sides are 8 and 8 is cut. Area of that triangle is 32.
100-32 is 68.
IMO C

Note : 1min 37sec. But could have solved way quicker if had i realized the shape _________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Senior Manager  G
Joined: 28 Jun 2019
Posts: 470
Re: What is the area of the figure above?  [#permalink]

### Show Tags

As we see in the figure, we could have a squire with sides 10.but the shape is not perfect.
So the area of the shape is less than 100=10*10.
In deed we got a triangle out of the shape whose area is 8*8/2=32
So,100-32=68
Option C

Posted from my mobile device
_________________
Always waiting Re: What is the area of the figure above?   [#permalink] 21 Aug 2019, 12:50
Display posts from previous: Sort by

# What is the area of the figure above?  