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