02 Nov 2009
… to do geometry for the GMAT

… to do geometry for the GMAT
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Category: GMAT, HOW TO's

Tricky geometry for the GMAT explained from the basics up.

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While geometry is not officially on the GMAT, if found during practice test that it regularly comes up, particularly in the medium to hard questions. Saying that, only a few geometrical concepts are tested. Here they are below:

Triangles

There are 4 types of triangles that you need to learn for the GMAT (actually I think that there are only 4 types of triangles overall).

Equilateral Triangle

The Equilateral Triangle is a triangle where all the sides and all the angles are equal. Since all the angles in a triangle must add up to 180° then each angle is always 60° regardless of the length of the sides (which are of course all equal too).

Isosceles Triangle

The Isosceles Triangles has two sides of equal length (thus two identical angles). Easy stuff so far.

Right- Angled Triangle

Seems to be a favourite on the GMAT, lots of questions on that one. A right-angles triangle has a right angle in it (90°) and thus the Pythagorean Theorem applies to it.  More on that subject a bit later.

Scalene Triangle

That is a triangle which has nothing equal whatsoever, all sides and all angles are all different.

Pytha

Circles

Circles are another big favourite on the GMAT, you will often see questions about triangles within circles to make it even more fun…

To understand the basics of circles we only need a few basic facts. These are the ones you need to know.

Circumference = the distance around the edge of the circle.

Diameter = a line across the widest part of a circle that passes through the centre.

Radius = 1/2 the diameter.

The diameter is ALWAYS approximately 3 times smaller than the circumference!
Or to put it another way, the circumference is approximately 3 times bigger than the diameter. To get the exact answer we have to multiply the diameter by ∏ (3.14). The GMAT is always multiple choice and thus dividing by 3 will generally get you a close enough answer to be able to do the question. The radius is simply half the diameter.

Formulas

The important formulas to know for the GMAT are here below. Remember that the GMAT doesn’t always give you all the measurements in the same units.

Area Formulas:

square = a 2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2)

circle = pi r 2


Perimeter Formulas:

square = 4a

rectangle = 2a + 2b

triangle = a + b + c   

Volume Formulas:

cube = a 3

rectangular prism = a b c

cylinder = b h = pi r 2 h

sphere = (4/3) pi r 3

The GMAT will not have many volume areas but they do come up every so often.

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