# Formulas for Math on the CSET®: Geometry and Measurement

Geometry and measurement are areas of math in which you’re urged to not be inaccurate. This, somehow, seems to make it easier to make mistakes. Too often, errors come from not knowing how to handle the different types of equations so it is very important for you to be familiar with these equations.

If you’re preparing for Math on the CSET® Multiple Subjects Test, there’s a 100% chance that you will be finding geometry and measurement questions there. At Union Test Prep, we have reproduced the following set of geometry formulas so you can practice with them. Check this out:

Free CSET® Math Study Materials

Formula Chart for Number Sense, Algebra, and Statistics Problems

## Geometry and Measurement Formulas

Category Formula Symbols Comment
Measurement $$Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF$$ Du = Desired unit
Su = Starting unit
CF = Conversion Factor
Multiple Steps may
be needed.
Measurement $$d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}$$ d = Distance between two points
$$y_n$$ = y value at point n
$$x_n$$ = x value at point n

Measurement $$\Sigma \theta = (n-2) \cdot 180^\circ$$ $$\Sigma \theta$$ = sum of interior angles
n = number of sides of polygon

Measurement $$a^2+b^2=c^2$$ a, b = legs of a right triangle
c = hypotenuse of a right triangle
Pythagorean Theorem
Perimeter $$C = 2 \cdot \pi \cdot r$$
$$C = \pi d$$
C = Circumference (perimeter) of a circle
d = Diameter

Perimeter $$s = r \cdot \theta$$ s = arc length
$$\theta$$ = Central angle (in radians)

Perimeter $$P = s_1+s_2+s_3$$ P = Perimeter of a triangle
$$s_n$$ = length of side n

Perimeter $$P = 4 \cdot s$$ P = Perimeter of a square
s = length of a side

Perimeter $$P = (2 \cdot l)+(2 \cdot w)$$ P = Perimeter of a rectangle
l = Length of rectangle
w = Width of rectangle

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

Area $$A= \dfrac{1}{2} b \cdot h$$ A = Area of a triangle
b = Base
h = height

Area $$A=s^2$$ A = Area of a square
s = Side length

Area $$A = l \cdot w$$ A = Area of a rectangle
l = Length
w = Width

Area $$A = h \cdot \dfrac{(b_1+b_2)}{2}$$ A = Area of a trapezoid
$$b_n$$ = Base n
h = Height

3-Dimensional
Objects
$$SA = \Sigma A_{fi}$$ SA = Surface area of a prism
$$A_{fi}$$ = Area of face i

3-Dimensional
Objects
$$SA = 2B + (C \cdot h)$$ SA = Surface area of a cylinder
B = Area of the base
C = Circumference of the base
h = height

3-Dimensional
Objects
$$SA = 4 \cdot \pi \cdot r^2$$ SA = Surface area of a sphere
r = Radius of the sphere

3-Dimensional
Objects
$$V = l \cdot w \cdot h$$ V = Volume of a rectangular prism
l = Length
w = Width
h = height

3-Dimensional
Objects
$$V = \dfrac{1}{3} \cdot (l \cdot w \cdot h)$$ V = Volume of a pyramid
l = Length
w = Width
h = Height

3-Dimensional
Objects
$$V = \pi \cdot r^2 \cdot h$$ V = Volume of a cylinder
$$V = \dfrac{4}{3} \cdot (\pi \cdot r^3)$$ V = Volume of a sphere