10.10.4: Formula Review

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Formula Review

10.2 Angles

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

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

10.4 Polygons, Perimeter, and Circumference

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

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

$S = (n - 2) 180^{\circ} .$

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

$a = \frac{(n - 2) 180^{\circ}}{n} .$

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

$b = \frac{360^{\circ}}{n} .$

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

10.6 Area

The area of a triangle is given as $A = \frac{1}{2} b h,$ 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 $A = l w .$

The area of a parallelogram is $A = b h .$

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

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.
$A = \frac{1}{2} b h,$ where $b$ is the base and $h$ is the height.

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

The area of a circle is given as $A = π r^{2},$ 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, $S A = 2 B + p h,$ 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 $S A = 2 π r^{2} + 2 π r h .$

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

10.8 Right Triangle Trigonometry

The Pythagorean Theorem states

$a^{2} + b^{2} = c^{2}$

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

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