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# Formulas for Math on the TASC Test–Geometry

The key to mastering geometry for the TASC Test is being able to picture in your head how the shape in the problem looks. That’s easier said than done, and the best way to hone your skill is by solving actual problems. Once you have a clear idea of the problem, solving it is actually pretty easy—you just need to apply the proper equation.

We want to help you train both of these skills, so go ahead and solve the sample geometry problems we have for you using the following formula sheet! On a positive side note, most of these equations will be also available to you during the test—how cool is that?

Also, look for our other formula charts for the TASC Math Test here:

Formulas for Math on the TASC Test–Algebra

Formulas for Math on the TASC Test–Statistics and Probability

## Basic Geometry Formulas for the TASC Math Test

Category Formula Symbols Comment
Coordinate
Geometry
$$(x_m, y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$$ $$x_m= x$$ value at midpoint
$$y_m= y$$ value at midpoint
$$x_n = x$$ value at point $$n$$
$$y_n= y$$ value at point $$n$$
Found in the formula
sheet on the test.
Coordinate
Geometry
$$d=\sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}$$ $$d$$ = distance between two points
$$y_n =y$$ value at point $$n$$
$$x_n =x$$ value at point $$n$$
Found in the formula
sheet on the test
Coordinate
Geometry
$$m=\frac{(y_2-y_1)}{(x_2-x_1)}$$ $$m$$ = slope
$$y_n$$ = dependent variable at point $$n$$
$$x_n$$ = independent variable at point $$n$$
This is a rearranged
version of the point-
slope form. Found on
the formula sheet on
the test.
Geometry $$C=2\pi r = \pi d$$ $$C$$ = circumference of a circle.
$$r$$ = radius
$$d$$ = diameter
$$\pi = 3.14$$

Geometry $$s=r\theta$$ $$s$$ = arc length
$$r$$ = radius
$$\theta$$ = central angle, in radians

Geometry $$A=\pi \cdot r^2$$ $$A$$ = area of a circle
$$r$$ = radius

Geometry $$A=\frac{1}{2}b \cdot h$$ $$A$$ = area of a triangle
$$b$$ = base
$$h$$ = height

Geometry $$A=s^2$$ $$A$$ = area of a square
$$s$$ = side length

Geometry $$A=l \cdot w$$ $$A$$ = area of a rectangle
$$l$$ = length
$$w$$ = width

Geometry $$A= h \cdot \frac{(b_1+b_2)}{2}$$ $$A$$ = area of a trapezoid
$$b_n$$ = base $$n$$
$$h$$ = height

Geometry $$V=l \cdot w \cdot h$$ $$V$$ = volume of rectangular prism
$$l$$ = length
$$w$$ = width
$$h$$ = height

Geometry $$V = \frac{1}{3}(l \cdot w \cdot h)$$ $$V$$ = volume of a pyramid
$$l$$ = length
$$w$$ = width
$$h$$ = height
Found in the formula
sheet on the test.
Geometry $$V=\pi \cdot r^2 \cdot h$$ $$V$$ = volume of a cylinder
$$r$$ = radius
$$h$$ = height
Found in the formula
sheet on the test.
Geometry $$V=\frac{4}{3} \cdot \pi \cdot r^3$$ $$V$$ = volume of a sphere
$$r$$ = radius
Found in the formula
sheet on the test.
Geometry $$V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h$$ $$V$$ = volume of a cone
$$r$$ = radius
$$h$$ = height
Found in the formula
sheet on the test.

## More Geometry Formulas for the TASC Math Test

These are all on the formula sheet you will be given during the test.

### Trigonometric Identities

$\text{sin } \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{\text{csc }\theta}$ $\text{cos } \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{1}{\text{sec }\theta}$ $\text{tan } \theta = \frac{\text{sin } \theta }{\text{cos }\theta } = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{\text{cot }\theta}$

### Angles

#### Central Angle

$m\angle \text{AOB} = m \overset{\frown}{\text{AB}}$

#### Inscribed Angle

$m\angle \text{ABC} = \frac{1}{2} m \overset{\frown}{\text{AC}}$

#### Intersecting Chords Theorem

$A \cdot B = C \cdot D$