10.9.3: Formula Review
10.2 Angles
To translate an angle measured in degrees to radians, multiply by \(\frac{\pi}{180}\).
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 \(P=2 L+2 W\), twice the length \(L\) plus twice the width \(W\).
The sum of the interior angles of a polygon with \(n\) sides is given by
\[S=(n-2) 180^{\circ} . \nonumber \]
The measure of each interior angle of a regular polygon with \(n\) sides is given by
\[a=\frac{(n-2) 180^{\circ}}{n} . \nonumber \]
To find the measure of an exterior angle of a regular polygon with \(n\) sides we use the formula
\[b=\frac{360^{\circ}}{n} . \nonumber \]
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 \(A=\frac{1}{2} b h\), 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 \(A=\pi r^2\), 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, \(S A=2 B+p h\), 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 \(S A=2 \pi r^2+2 \pi r h\).
The volume of a right cylinder is given as \(V=\pi r^2 h\).
10.8 Right Triangle Trigonometry
The Pythagorean Theorem states
\[a^2+b^2=c^2 \nonumber \]
where \(a\) and \(b\) are two sides (legs) of a right triangle and \(c\) is the hypotenuse.