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# each trapezoid in the figure below is congruent to trapezoid abdc. 4 trapezoids are connected. trapezoid a b c d is connected to trapezoid b d g h at side b d. another trapezoid is on top of trapezoid a b c d and connects at side c d. another trapezoid is on top of trapezoid b d g h and connects at side d g. the length of side c a is 3 centimeters, the length of a b is 4 centimeters, and the length of side c d is 6 centimeters. what is the perimeter of hexagon acefgh? 28 cm 32 cm 36 cm 64 cm

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### James

Guys, does anyone know the answer?

get each trapezoid in the figure below is congruent to trapezoid abdc. 4 trapezoids are connected. trapezoid a b c d is connected to trapezoid b d g h at side b d. another trapezoid is on top of trapezoid a b c d and connects at side c d. another trapezoid is on top of trapezoid b d g h and connects at side d g. the length of side c a is 3 centimeters, the length of a b is 4 centimeters, and the length of side c d is 6 centimeters. what is the perimeter of hexagon acefgh? 28 cm 32 cm 36 cm 64 cm from EN Bilgi.

## Each trapezoid in the figure below is congruent to ## Each trapezoid in the figure below is congruent to What is the perimeter of hexagon ACEFGH? trapezoid ABDC. 28 cm 32 cm 36 cm 64 cm

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## Trapezoid Flashcards

Start studying Trapezoid. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Trapezoid

Trapezoids

Click card to see definition 👆

A trapezoid has ONLY ONE set of parallel sides.

When proving a figure is a trapezoid, it is necessary to prove

that two sides are parallel and two sides are NOT parallel.

Click again to see term 👆

The angles on the same side of a leg are called adjacent angles such as ∠A and ∠D are supplementary. For the same reason, ∠B and ∠C are supplementary.

Click card to see definition 👆

... Click again to see term 👆

1/34 Created by chemgeoTEACHER

### Terms in this set (34)

Trapezoids

A trapezoid has ONLY ONE set of parallel sides.

When proving a figure is a trapezoid, it is necessary to prove

that two sides are parallel and two sides are NOT parallel.

The angles on the same side of a leg are called adjacent angles such as ∠A and ∠D are supplementary. For the same reason, ∠B and ∠C are supplementary. Area of Trapezoid The midsegment of a trapezoid is:

parallel to both bases

has length equal to the average of the length of the bases The median (also called the mid-segment) of a trapezoid is a segment that connects the midpoint of one leg to the midpoint of the other leg. Theorem:

The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

(True for ALL trapezoids.)

Theorems:

1. A trapezoid is isosceles if and only if the base angles are congruent.

2. A trapezoid is isosceles if and only if the diagonals are congruent.

3. If a trapezoid is isosceles, the opposite angles are supplementary.

Never assume that a trapezoid is isosceles unless you are given (or can prove) that information.

Bases - The two parallel lines are called the bases

The Legs - The two non parallel lines are the legs. Isosceles Trapezoid I have:

1. only one set of parallel sides

2. base angles congruent

3. legs congruent

4. diagonals congruent

5. opposite angles supplementary

First, let us make the trapezoid. You start with a triangle of sides a, b, and c where the sides a and b meet to form a right angle.

Then put a second triangle below the first such that side a is an extension of the other triangles b side. Second, put a second triangle below the first such that side a is an extension of the other triangles b side. Third, connect the end of side a at the top with side b on the bottom to create the trapezoid. To find the length of the diagonal, we need to use the pythagorean Theorem. Therefore, we need to sketch the following triangle within the trapezoid: ABCD

we know that the base of the triangle has length of 9 m. By subtracting the top the trapezoid from the bottom of the trapezoid, we get:

12 m - 6 m = 6 m

Dividing by two, we have the length of each additional side on the bottom of the trapezoid. 6m/2 = 3madding these two values together, we get 9 m .The formula for the length of the diagonal AC uses the Pythagorean Theorem:

AC2 = AE 2 + EC2, where E is the point between a and D representing the base of the triangle.

AC2 = (9m)2 + (4 m)2

AC2 = square of 97 m In trapezoid ABCD:

(1) The degree measure of the four angles add up to 360 degrees. This is actually true of any quadrilateral. Let lower case letters a, b, c and d = the angles of trapezoid ABCD.

Then: a + b + c + d = 360 degrees. Source : quizlet.com

## What is the area of the trapezoid shown? : Data Sufficiency (DS)

Trapezoid.JPG What is the area of the trapezoid shown? (1) Angle A = 120 degrees (2) The perimeter of trapezoid ABCD = 36. GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

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Data Sufficiency (DS)

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What is the area of the trapezoid shown?

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PathFinder007

Manager

Joined: 10 Mar 2014

Posts: 155

What is the area of the trapezoid shown? [#permalink]

01 Aug 2014, 07:54 7 Kudos 39 Bookmarks 00:00 A B C D E

### SHOW TIMER STATISTICS

Attachment: Trapezoid.JPG [ 30.38 KiB | Viewed 29664 times ]

What is the area of the trapezoid shown?

(1) Angle A = 120 degrees

(2) The perimeter of trapezoid ABCD = 36. G

mikemcgarry

Magoosh GMAT Instructor

Joined: 28 Dec 2011

Posts: 4468

Re: What is the area of the trapezoid shown? [#permalink]

01 Aug 2014, 09:56 9 Kudos 6 Bookmarks Expert Reply

PathFinder007 wrote:

What is the area of the trapezoid shown?

(1) Angle A = 120 degrees (2) The perimeter of trapezoid ABCD = 36.

Dear PathFinder007,

I'm happy to respond.

Remember, the BIG question on GMAT Data Sufficiency is not "what is the answer?" but rather, "do we have enough information to determine the answer?" This is very subtle --- the sufficiency question is not, "could you in particular find the answer from the information?"; it's really more: "could the ideal math student, given this information, find the answer?" That's the sufficiency question.

Here's a blog that discusses some implication for DS in Geometry:

http://magoosh.com/gmat/2012/gmat-data- ... nce-rules/

So let's look at this:

Statement #1: if angle A = 120, then angle A = angle B = 120, and angle C = angle D = 60. Every angle is determined, and some lengths are specified, so the size and shape are completely determined. That means, the area is completely determined. We don't need to find it. It's enough to know that it's completely determined. Sufficient.

Statement #2: We know AC = BD = 8, because it's an isosceles trapezoid. If we are given the perimeter, then we also know the length of CD, the fourth side. If all four sides are know, that locks the shape in place, determining all the angles and the size and the shape. Again, this completely determines the area. Sufficient.

Both statements sufficient alone. Answer = (D). We can answer the entire DS question without even bothering about calculating the area.

Now, suppose we had a similar PS question in which we had to find the area of this isosceles trapezoid.

Attachment: isosceles trapezoid, 60-120.JPG [ 22.17 KiB | Viewed 29542 times ]

By the properties of the 30-60-90 triangle, which are explained here:

http://magoosh.com/gmat/2012/the-gmats- ... triangles/

we know that CE = FD = 4, and of course EF = 6, making the perimeter 36.

AE = BF = 4sqrt(3) 4sqrt(3)

Area of rectangle EABF =

24sqrt(3) 24sqrt(3)

Area of triangle ACE = area of triangle BDF =

8sqrt(3) 8sqrt(3)

Area of isosceles trapezoid CABD =

40sqrt(3) 40sqrt(3)

Does all this make sense?

Mike _________________ Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

### General Discussion

babulsaha

Intern

Joined: 30 Jul 2014

Posts: 2

Re: What is the area of the trapezoid shown? [#permalink]

01 Aug 2014, 09:33

Diagram is in the attached file.

Area of trapezoid ABCD = ½ X (b1+b2) X Height= ½ X (6+14) X 4√3 =1/2 X 20 X 4√3 = 40√3 cm

Given that angle CAB=120 and Perimeter of ABCD = 36 cm. So CD = 36 – AC – AB – BD

= 36 – 8 – 6 – 8 =14 cm

So we extend A to E and F. Now Angle CAE = 180 – 120 = 60, angle AEC = 90 and angle ACE = 30.

So Triangle ACF is equilateral triangle. we connect CE

As per Pythagoras theorem, AE square + CE square = AC square

=> 4 square + 4√3 square = 8 square

=> 16 + 48 = 64

So here , AE = 4 cm and CD = 4√3 = Height

Attachments

trapeziod.docx [13.99 KiB]

B

karanb

Intern

Joined: 24 Feb 2013

Posts: 10

Location: United States (CA)

GMAT 1: 710 Q48 V40