### Formula Review

## 10.2 Angles

To translate an angle measured in degrees to radians, multiply by $\frac{\pi}{180}\text{.}$

To translate an angle measured in radians to degrees, multiply by $\frac{180}{\pi}.$

## 10.4 Polygons, Perimeter, and Circumference

The formula for the perimeter $P$ of a rectangle is $P=2L+2W$, twice the length $L$ plus twice the width $W$.

The sum of the interior angles of a polygon with $n$ sides is given by

The measure of each interior angle of a regular polygon with $n$ sides is given by

To find the measure of an exterior angle of a regular polygon with $n$ sides we use the formula

The circumference of a circle is found using the formula $C=\pi d,$ where $d$ is the diameter of the circle, or $C=2\pi r,$ where $r$ is the radius.

## 10.6 Area

The area of a triangle is given as $A=\frac{1}{2}bh,$ where $b$ represents the base and $h$ represents the height.

The formula for the area of a square is $A=s\cdot s$ or $A={s}^{2}.$

The area of a rectangle is given as $A=lw.$

The area of a parallelogram is $A=bh.$

The formula for the area of a trapezoid is given as $A=\frac{1}{2}h\left(a+b\right).$

The area of a rhombus is found using one of these formulas:

- $A=\frac{{d}_{1}{d}_{2}}{2},$ where ${d}_{1}$ and ${d}_{2}$ are the diagonals.
- $A=\frac{1}{2}bh,$ where $b$ is the base and $h$ is the height.

The area of a regular polygon is found with the formula $A=\frac{1}{2}ap,$ where $a$ is the apothem and $p$ is the perimeter.

The area of a circle is given as $A=\pi {r}^{2},$ where $r$ is the radius.

## 10.7 Volume and Surface Area

The formula for the surface area of a right prism is equal to twice the area of the base plus the perimeter of the base times the height, $SA=2B+ph,$ where $B$ is equal to the area of the base and top, $p$ is the perimeter of the base, and $h$ is the height.

The formula for the volume of a rectangular prism, given in cubic units, is equal to the area of the base times the height, $V=B\cdot h,$ where $B$ is the area of the base and $h$ is the height.

The surface area of a right cylinder is given as $SA=2\pi {r}^{2}+2\pi rh.$

The volume of a right cylinder is given as $V=\pi {r}^{2}h.$

## 10.8 Right Triangle Trigonometry

The Pythagorean Theorem states

where $a$ and $b$ are two sides (legs) of a right triangle and $c$ is the hypotenuse.