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# Geometry and Measurement Formulas for the TSIA2

If you want to have the skills needed to succeed in Math, it’s very important that you remember the specific formulas needed to solve each problem. That becomes particularly important when solving the Geometry and Measurement problems in the TSIA2. Here at Union Test Prep, we have what you need. In the following chart you’ll find the Geometry and Measurement Formulas you’ll need for the TSIA2.

You’ll also want to check out our other two math formula charts for this test:

Formulas for Algebra and Functions

Formulas for Data Analysis, Statistics, and Probability

You can practice using these formulas by accessing the math sections of our free TSIA2 prep materials.

## Geometry and Measurement Formulas

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 $$y=m \cdot x + b$$ y = dependent variable
m = slope
x = independent variable
b = y-axis intercept
Slope-Intercept Form:
Try to convert any given
linear equation to this form.
The XY Plane $$m=\dfrac{(y_2-y_1)}{(x_2-x_1)}$$ m = slope
$$y_n$$ = dependent variable (at point n)
$$x_n$$ = independent variable (at point n)
This is a rearrangement 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
Poit-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 value at point n
$$x_n$$ = x value at point n

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 $$C=2 \cdot \pi \cdot r$$
$$C=\pi \cdot d$$
C = Circumference (perimeter) of a circle
r = radius
d = diameter

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

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

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

Triangles $$A=\frac{1}{2}b \cdot h$$ 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
Pythagorean Theorem
Quadrilaterals $$P=4 \cdot s$$ P = Perimeter of a square
s = length of a side

Quadrilaterals $$P= (2 \cdot l)+(2 \cdot w)$$ P Perimeter of a rectangle
l = length
w = width

Quadrilaterals $$A=s^2$$ A = Area of a square
s = length of a side

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
$$b_b$$ = base n
h = height

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

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

3-Dimensional
Objects
$$V= \frac{1}{3} (l \cdot w \cdot h)$$ 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
r = radius
h = height

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
$$V= \frac{4}{3} \cdot \pi \cdot r^3$$ V = Volume of a sphere
r = radius

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