Contemporary Mathematics

# Formula Review

### 10.2Angles

To translate an angle measured in degrees to radians, multiply by $π180.π180.$

To translate an angle measured in radians to degrees, multiply by $180π.180π.$

### 10.4Polygons, Perimeter, and Circumference

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

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

$S=(n−2)180∘.S=(n−2)180∘.$

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

$a=(n−2)180∘n.a=(n−2)180∘n.$

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

$b=360∘n.b=360∘n.$

The circumference of a circle is found using the formula $C=πd,C=πd,$ where $dd$ is the diameter of the circle, or $C=2πr,C=2πr,$ where $rr$ is the radius.

### 10.6Area

The area of a triangle is given as $A=12bh,A=12bh,$ where $bb$ represents the base and $hh$ represents the height.

The formula for the area of a square is $A=s⋅sA=s⋅s$ or $A=s2.A=s2.$

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

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

The formula for the area of a trapezoid is given as $A=12h(a+b).A=12h(a+b).$

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

• $A=d1d22,A=d1d22,$ where $d1d1$ and $d2d2$ are the diagonals.
• $A=12bh,A=12bh,$ where $bb$ is the base and $hh$ is the height.

The area of a regular polygon is found with the formula $A=12ap,A=12ap,$ where $aa$ is the apothem and $pp$ is the perimeter.

The area of a circle is given as $A=πr2,A=πr2,$ where $rr$ is the radius.

### 10.7Volume 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, $SA=2B+ph,SA=2B+ph,$ where $BB$ is equal to the area of the base and top, $pp$ is the perimeter of the base, and $hh$ 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, $V=B⋅h,V=B⋅h,$ where $BB$ is the area of the base and $hh$ is the height.

The surface area of a right cylinder is given as $SA=2πr2+2πrh.SA=2πr2+2πrh.$

The volume of a right cylinder is given as $V=πr2h.V=πr2h.$

### 10.8Right Triangle Trigonometry

The Pythagorean Theorem states

$a2+b2=c2a2+b2=c2$

where $aa$ and $bb$ are two sides (legs) of a right triangle and $cc$ is the hypotenuse.

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