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, study guide, and flashcards for the GRE Quantitative Reasoning Test.
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:
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 
SlopeIntercept Form: Try to convert any given linear equation to this format. 
The XY Plane  \(m = \dfrac{Y2y_1}{x_2x_1}\)  m = slope \(y_n\) = dependent variable (point n) \(x_n\) = independent variable (point n) 
This is a rearranged version of the pointslope form. 
The XY Plane  \(y  y_1 = m(xx_1)\)  \((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope 
Point slope form 
The XY Plane  \(d = \sqrt{(y_2y_1)^2 + (x_2x_1)^2}\)  d = distance between two points \(y_n\) = y score at point n \(x_n\) = x score at point n 

Polygons  \(\Sigma \theta = (n2)\cdot 180^\circ\)  \(\Sigma \theta\) = 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  \((xh)^2 + (yk)^2 = r^2\)  (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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