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Formulas for the Geometry Questions on the GRE® Quantitative Reasoning Test

Geometry is one of the areas of math in which you need to sort out and remember all sorts of formulas for area, volume, perimeter, and a variety of other measurements.

If you are studying for the Geometry Questions on the GRE® Quantitative Reasoning Test, Union Test Prep has just the right resource for you! In the following chart, you’ll find the most important formulas you will need when you are solving this type of problem.

Also, check out our free practice questions and free flashcards for the GRE® Quantitative Reasoning Test.

And learn even more with our free study guide.

Remember that this chart only shows formulas for one part of the test: Geometry. Access our other three formula charts for the GRE® Quantitative Reasoning section, here:

Arithmetic

Algebra

Data Analysis

Category Formula Symbols Comment
The XY Plane \(Ax+By =C\) A, B, C = any real number
y = dependent variable
x = independent variable
Standard form
The XY Plane \(y = mx + b\) y = dependent variable
m = slope
x = independent variable
b = y axis intercept
Slope-Intercept Form:
Try to convert
any given linear
equation to this
format.
The XY Plane \(m = \dfrac{Y-2-y_1}{x_2-x_1}\) m = slope
\(y_n\) = dependent variable (point n)

\(x_n\) = independent variable (point n)
This is a rearranged
version of the
point-slope form.
The XY Plane \(y - y_1 = m(x-x_1)\) \((x_1, y_1)\) = point on the line
y = dependent variable
x = independent variable
m = slope
Point slope form
The XY Plane \(d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}\) d = distance between two points
\(y_n\) = y score at point n
\(x_n\) = x score at point n
 
Polygons \(\Sigma \theta = (n-2)\cdot 180^\circ\) \(\Sigma \theta\) = sum of interior angles
n = number of sides of a polygon
 
Triangles \(P = s_1 + s_2 + s_3\) P=Perimeter of a triangle
\(s_n\) = side length
 
Triangles \(A = \frac{1}{2}bh\) A = Area of a triangle
b = base
h = height
 
Triangles \(a^2 + b^2 = c^2\) a,b = legs of a right triangle
c = hypotenuse of a right triangle
 
Quadrilaterals \(P = 4 \cdot s\) P = Perimeter of a square
s = side length
 
Quadrilaterals \(P = 2l + 2w\) P = Perimeter of a rectangle
l = length
w = width
 
Quadrilaterals \(A = s^2\) A = Area of a square
s = side length
 
Quadrilaterals \(A = l \cdot w\) A = Area of a rectangle
l = length
w = width
 
Quadrilaterals \(A = h \cdot \dfrac{b_1+b_2}{2}\) A = Area of a trapezoid
\(b_n\) = base n
h = height
 
Circles \((x-h)^2 + (y-k)^2 = r^2\) (h,k) = center of a circle
r = radius
Standard form
of a circle
Circles \(x^2 +y^2 + Ax +By + C = 0\) x, y =variables
A, B, C = constants
General form
of a circle
Circles \(C = 2\pi r = \pi d\) C = Perimeter of a circle
r = radius
d = diameter
\(\pi\) = 3.14
 
Circles \(s= r\theta\) s = arc length
r = radius
\(\theta\) = central angle (radians)
 
Circles \(A = \pi r^2\) A = Area of a circle
r = radius
 
Rectangular
Prisms
\(V = l\cdot w \cdot h\) V = Volume of a rectangular prism
l = length
w = width
h = height
 
Rectangular
Prisms
\(SA = \Sigma A_{fi}\) SA = Surface Area of a Prism
\(A_{fi}\) = Area of face i
 
Pyramids \(V = \frac{1}{3} (lwh)\) V = Volume of a pyramid
l = length
w = width
h = height
 
Pyramids \(SA = \Sigma A_{fi}\) SA = Surface Area of a Pyramid
\(A_{fi}\) = Area of face i
 
Circular
Cylinders
\(V = \pi r^2 h\) V = Volume of a cylinder
r = radius
h = height
 
Circular
Cylinders
\(SA = 2B +C\cdot h\) SA = Surface Area of a cylinder
B = Area of the Base
C = Circumference of the Base
h = height
 
Spheres \(V = \frac{4}{3} \pi r^3\) V = Volume of a sphere
r = radius
 
Spheres \(SA = 4 \pi r^2\) SA = Surface Area of a sphere
r = radius of the sphere
 

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