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Trigonometry and Calculus: Area
The concept of area is important at all levels of mathematics. A knowledge
of calculus is helpful in solving many of the problems below, such as
Building a Sandbox.
Other problems, like
Another Problematic
Pizza, require trigonometry in the solution.
For background information elsewhere on our site, explore the
High School Trigonometry
and Calculus
areas of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Trigonometry and
Calculus (Single Variable)
in our Internet Mathematics Library.
Access to these problems requires a Membership.

Another Problematic Pizza
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the area of a triangular piece of pizza.
... more>>

Be My Valentine
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the areas of two heartshaped valentines.
... more>>

Building a Sandbox
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the maximum area for a triangularshaped sandbox.
... more>>

Cutting the Cookie
 Leigh Nataro

Trig/Calc, difficulty level 2. Where should you cut a circular cookie so its area is in a ratio of 1:2 ?
... more>>

An Eggstra Special Problem
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a crosssection of an egg given some dimensions of the crosssection.
... more>>

Ellipse Areas
 Leigh Nataro

Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b.
... more>>

Environmentally Friendly
 Leigh Nataro

Trig/Calc, difficulty level 2. What dimensions for a given page will use the least amount of paper?
... more>>

George's Gutters
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a gutter.
... more>>

The Growing Snowflake
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the limit for the area of the Koch snowflake.
... more>>

A Holiday Card
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the ratio of the red area to the green area as the number of squares approaches infinity.
... more>>

How Large Is The Yard?
 Leigh Nataro

Trig/Calc, difficulty level 2. Given three sides and two included angles, find the area of my parents' quadrilateralshaped backyard.
... more>>

Irregular Acreage
 Leigh Nataro

Trig/Calc, difficulty level 2. Based on the given information, find the missing length of a lot in the shape of a quadrilateral.
... more>>

Job Interview at the CanCan Company
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the smallest amount of tin needed to make a can that can hold 12 cubic inches.
... more>>

Kite Construction
 Leigh Nataro

Trig/Calc, difficulty level 2. Given some information about the dimensions of a kite, find its area.
... more>>

Let the Sunshine In
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the dimensions of a window designed to let in the maximum amount of sunshine.
... more>>

Managing a Mall
 Leigh Nataro

Trig/Calc, difficulty level 2. Find how many square feet there are in a quadrilateralshaped store.
... more>>

One Area  Many Solutions
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices.
... more>>

The Oval Braided Rug
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a shaded portion of an ellipse.
... more>>

A Parabola Proof
 Leigh Nataro

Trig/Calc, difficulty level 3. Prove that the area of a parabola is 2/3 the product of its width and height.
... more>>

A Picture Is Worth A Thousand Words
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the ratio of the area of the overlapping region to the area of nonoverlapping regions of two circles.
... more>>

Pie Puzzler
 Paul Robinson

Trig/Calc, difficulty level 2. Where should a pie wedge be cut to divide it into two pieces having the same area?
... more>>

A Problematic Pizza
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a specific region of a circle based on given information.
... more>>

The Seal of Dalvek
 Steve Earth

Trig/Calc, difficulty level 3. Discover the area of a circular segment based upon its circumference.
... more>>

The Square and the Line
 Leigh Nataro

Trig/Calc, difficulty level 1. Find the equation of the line that will split a unit square into two pieces that have equal areas.
... more>>

The SuperUltraMegaBig Cup
 Alvirne High School Calculus Class

Trig/Calc, difficulty level 3. What is the minimum cost to make a cup based on given information?
... more>>

The Super Yard XT
 Leigh Nataro

Trig/Calc, difficulty level 1. Based on information about the area of a regular polygonshaped play yard, find the length of one of the walls of the yard.
... more>>

The Triangle Inside an Angle
 Ramani Jv

Trig/Calc, difficulty level 5. Based on the given information, find the area of the smallest triangle contained within an angle.
... more>>

Triangles, Sines, and Areas
 Leigh Nataro

Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A).
... more>>

Your Interview Question Is...
 Leigh Nataro

Trig/Calc, difficulty level 3. If you want to minimize the surface area of a can with a fixed volume, what should be the ratio of the height to the radius?
... more>>
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