# approximating area under a curve   58 videos

• #### Using Sine to Calculate the Area of a Triangle

##### TrigonometryBasic Trigonometry

How to calculate the area of any triangle using two sides and an included angle.

area of a triangle sine
• #### Using Sine to Calculate the Area of a Triangle

##### PrecalculusBasic Trigonometry

How to calculate the area of any triangle using two sides and an included angle.

area of a triangle sine
• #### Area of Regular Polygons

##### GeometryArea

How to derive the formula to calculate the area of a regular polygon.

area apothem side hexagon isosceles triangle perimeter equilateral equiangular
• #### Area of Trapezoids

##### GeometryArea

How to derive the area of a trapezoid formula using the area of a rectangle.

trapezoid parallelogram base height
• #### Area of an Annulus

##### GeometryArea

How to derive the formula for the area of an annulus.

annulus donut radius region circle
• #### Area of Kites and Rhombuses

##### GeometryArea

How to derive the area formula of a kite based on the rectangle formula; how to calculate the area of a rectangle using diagonal lengths.

kite area diagonals consecutive sides vertex angle non vertex angle bisect perpendicular rhombus
• #### Average Value of a Function

##### CalculusThe Definite Integral

How to find the average value of a function over an interval [a,b].

average value antidifferentiation limits of integration functions area under a curve
• #### Area and Perimeter of Circles

##### Pre-AlgebraIntroductory Geometry

Vocabulary and formulas for the area of a circle

• #### Area With the Cross Product

##### PrecalculusSystems of Linear Equations and Matrices

How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.

cross product magnitude of vectors dot product angle between vectors area parallelogram
• #### Area and Perimeter of Rectangles

##### Pre-AlgebraIntroductory Geometry

Overview of area and perimeter formulas for parallelograms and rectangles

• #### Volume and Surface Area

##### Pre-AlgebraIntroductory Geometry

Vocabulary and formulas for surface area and volume of common solids

• #### Families of Polar Curves: Conic Sections

##### PrecalculusPolar Coordinates and Complex Numbers

How to describe the polar equations of conic sections.

polar graph polar equation polar curve conic sections focus origin pole parabola symmetric about the x axis parabola vertex
• #### Area and Perimeter of Triangles

##### Pre-AlgebraIntroductory Geometry

Understanding why the area of a triangle is 1/2 base times height

• #### Families of Polar Curves: Circles, Cardiods, and Limacon

##### PrecalculusPolar Coordinates and Complex Numbers

How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.

polar graph polar equation polar curve circles center radius completing the square
• #### Solving Formulas

##### GeometryArea

How to strategize about solving formulas for variables; how to solve the area of a rectangle formula for base and height; how to solve the area of a triangle formula for base and for height.

formulas isolating a variable rectangle area triangle area trapezoid area regular polygon area
• #### Curve Sketching with Derivatives

##### CalculusApplications of the Derivative

How to evaluate the limit of a function using continuity.

• #### Pythagorean Theorem Proofs

##### GeometryPythagorean Theorem

How to prove the Pythagorean Theorem using Algebra to show the area of the smaller square plus the area of four triangles is equal to the area of the larger square.

right triangle area of a square binomial squared area of a triangle side leg hypotenuse
• #### Pythagorean Theorem Proofs

##### TrigonometryPythagorean Theorem

How to prove the Pythagorean Theorem using Algebra to show the area of the smaller square plus the area of four triangles is equal to the area of the larger square.

right triangle area of a square binomial squared area of a triangle side leg hypotenuse
• #### Similarity and Volume Ratios

##### GeometrySimilarity

How to identify if two solids are similar and how to convert 1D ratios to surface area and volume ratios.

similarity volume ratios surface area
• #### An Important Limit

##### CalculusThe Derivative

How to interpret the value of a limit important in the derivative of exponential functions.

limits natural logarithm numerical approximation

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