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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.

### 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
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
d = diameter
$$\pi$$ = 3.14

Circles $$s= r\theta$$ s = arc length
$$\theta$$ = central angle (radians)

Circles $$A = \pi r^2$$ A = Area of a circle

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
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
Spheres $$SA = 4 \pi r^2$$ SA = Surface Area of a sphere