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 Your Progress

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.

Re: What is the area of the quadrilateral shown above? [#permalink]
04 Jan 2018, 21:13

1

This post received KUDOS

Draw a perpendicular forming two right angle triangle, now the figure has two right angle triangle and one rectangle.Both the triangles have same angle so the area will be same. By using pythagoras theorem find the height of the triangle i.e sqrt(3), now find the area of both the triangle and a rectangle. sqrt(3)/2+sqrt(3)/2+2*sqrt(3) = 3sqrt(3)

Re: What is the area of the quadrilateral shown above? [#permalink]
11 Jan 2018, 00:51

1

This post received KUDOS

Consider three equilateral triangles within quadrilateral,each with side measuring 2.Now Area for Equilateral triangle is (sqrt(3)/4)*(side)^2 and multiply it by 3 to get area for three equilateral triangle i.e whole quadrilateral.

Re: What is the area of the quadrilateral shown above? [#permalink]
23 Jan 2019, 07:43

Yes it can be considered as a trapezoid, since the two angles alpha are the same and are connected to the longer of the two bases.

Area: 0.5(Base 1 + Base 2) * height.

How do we get the height? The shorter base (length 2) must have its center where the longer base has its center due to the fact that both angles are equal. Thus, we derive that the longer base just extends the shorter base by (4-2 = 2). Split equally on each side, we can see the longer base composition of lengths 1 + 2 + 1.

If we look at the left part of the figure we have the upward sloping line with length 2. If we let fall a perpendicular from the connection of the upward sloping line and its vertex with the shorter base, we arrive exactly at the first part of the 1 + 2 + 1 composition of the longer base.

Thus we have a created triangle with a base 1 and hypotenuse 2. Since we also know that it has a 90-degree angle, we can deduct it must be a 30 - 60 - 90 triangle. (Remainder: Side lengths of a 30 - 60 - 90 triangle are 1:2:sqrt(3). Thus the height of the triangle is sqrt(3) which equals the height of the trapezoid.

Plug in the formula.

greprepclubot

Re: What is the area of the quadrilateral shown above?
[#permalink]
23 Jan 2019, 07:43