To solve the GMAT Quantitative Reasoning questions or the geometry questions in the GMAT exam, it’s essential you are thorough with the GMAT Math Geometry formulas as it makes solving questions faster and easier. Here is an article that covers all the basic geometry formulas you need to ace Geometry questions in the quant section.

So let’s take a look at this GMAT Math Geometry formulas list.

Geometry Questions

Geometry Solutions

Perimeter Formulas

ShapeFormulaWhere, P = Perimeter and
SquareP = 4ss = sides
RectangleP = 2l + 2wl = length w = width
ParallelogramP = 2l + 2wl = length w = width
Trapezoid or TrapeziumP = s {1} + s {2} + b {1} + b {2}s {1} and s {2} are two sides and b {1} and b {2} are the two bases of the figure.
TriangleP = s {1} + s {2} + bs {1} and s {2} are two sides andb = base
RhombusP = 4ll = length

Area Formulas

ShapeFormulaWhere A = Area and
TriangleA = {1} / {2} times b times hb = baseh = vertical height
SquareA = a ^ {2}a = length of side
RectangleA = w times hw = widthh = height
ParallelogramA = b times hb = baseh = vertical height
Trapezoid or TrapeziumA = {1} / {2} (a + b) times ha, b = length if two sides of the figureh = vertical height
CircleA = pi.r^{2}r = radius
EllipseA = pi.aba, b = longest and shortest radius of the figure
Sector of a CircleA = {1} / {2} r ^ {2} thetar = radiustheta = angle in radians
Regular n-polygon  A = {1}/{4} times n times a^{2} times cot {pi}/{n} n = number of sidesa = length of the sides

Surface Area Formulas

ShapeFormulaWhere S = Surface Area and
Rectangular SolidS = 2lh + 2wh + 2wll  = lengthh = height w = width
CubeS = 6s^{2}s = sides of the cube
Right Circular CylinderS = 2.pi times rh + 2.pi times r^{2}h = vertical height of the cylinderr = radius of the base
SphereS = 4.pi times r^{2}r  = radius
Right Circular ConeS = pi times r^{2} + pi.r times whole root of (r^{2} + h^{2})h = vertical heightr  = radius of the base
TorusS = pi^{2} times (R^{2} – r^{2})R = radius of the larger baser = radius of the smaller base

Volume Formulas

ShapeFormulaWhere V = Volume and
Rectangular SolidV = lwhl  = lengthh = height w = width
CubeV = s^{3}s = sides of the cube
Right Circular CylinderV = pi times r^{2}hh = vertical height of the cylinderr  = radius of the base
SphereV = {4}/{3} times pi.r^{3}r  = radius
Right Circular ConeV = {1}/{3} pi.r^{2}hh = vertical heightr = radius of the base
Square or Rectangular PyramidV = {1}/{3} lwhl  = length of the baseh = vertical height w = width of the base (In case of square, both l and w will be equal)

Circle

Circumference of a Circle

Circumference (C) = pi.d = 2 times pi.r

Where, d = Diameter and r = Radius

Area of a Circle

Area (A) = pi.r^{2}

Where, r = Radius

Pythagoras Theorem

The Pythagorean Theorem states that the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.

This implies that in the above Triangle, a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse of the triangle.

a^2 + b^2 = c^2

For any GMAT Arithmetic or Quantitative Reasoning problem, formulas are those fundamentals that help you to think and solve them with ease. Hence, memorizing these GMAT math geometry formulas thoroughly helps solve easy or even difficult problems faster. We have listed some important geometry formulas including surface area formulas, volume formulas, and formulas for GMAT Circles, that you need to know. However, you may also look for GMAT geometry formulas PDF online to get a better picture. But, make it a point to refer to credible resources or websites.  

GMAT Geometry Sample Questions 

1. In the figure below, line segment is parallel to CD. What is the value of “a”?

  1. 20
  2. 40
  3. 80
  4. 100
  5. 140

Answer: D

Explanation:

Since AB is parallel to CD, 

2×0+a0=1800…Equation (1)

Because Big angle + Small angle is 180 degrees.

Now DEC is a triangle, where sum of the all angles of a triangle is 180 degrees.

So, a0+x0+400=1800

a0+x0=1400…Equation (2)

Solving both the equations we get,

x = 40

so, a = 100.

Hence the answer is D.

2. In triangle ABC below, if AC = 12 inches, then what is the length of AB in inches?

Note: Figure not drawn to scale

  1. 3
  2. 6
  3. 62
  4. 66
  5. 18

Answer: D

Explanation:

Re-draw the diagram and label all the angles as mentioned below,

We can see the 30-60-90 triangle and 45-45-90 triangle.

In 30-60-90 triangle, sides are in the ratio of a-a3-2a

In 45-45-90 triangle, sides are in the ratio of a-a-a√2

ADC is 30-60-90 triangle, given that AC = 12

Hence the sides are, 6-63-12  

AD = 63

ADC is 45-45-90 triangle and AD= 63

So, the sides are, 63-63-66. So, AB length is 66 

Hence the answer is D.

Now that you are aware of almost all the GMAT math Geometry formulas, you’re better positioned to apply these formulas to the various Geometry questions that appear in your practice or mock tests and of course the actual exam. All the best!

FAQs

  1. How Can I Prepare for the GMAT Quant section?

The most important step to preparing for the GMAT Quant section is practising the Quant concepts. You can do so by attempting sample questions and GMAT mock tests. You can also look for GMAT Geometry Formulas PDF online to help you familiarize yourself with all geometry formulas. 

  1. How can I memorize geometry formulas for the GMAT Quant section? 

An easy way to memorize formulas for the GMAT Quant section is by creating a GMAT Geometry cheat sheet. A cheat sheet is nothing but a list of all the geometry formulas. You can place this cheat sheet on your mirror or any space that you visit on a regular basis. This will help you memorize the formulas in no time. 

  1. What is the surface area formula for a cube? 

The surface area formula for a rectangle solid is V = s^{3}, where s = sides of the cube. 

X

Talk to an expert?

Leave a Reply

Your email address will not be published.