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Contemporary Mathematics

Formula Review

Contemporary MathematicsFormula Review

Formula Review

10.2 Angles

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.

10.4 Polygons, 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.

10.6 Area

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.

10.7 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,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.

10.8 Right 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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