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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 heart-shaped valentines. ... more>>

Building a Sandbox - Leigh Nataro
Trig/Calc, difficulty level 3. Find the maximum area for a triangular-shaped 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 cross-section of an egg given some dimensions of the cross-section. ... 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' quadrilateral-shaped 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 Can-Can 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 quadrilateral-shaped 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 non-overlapping 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 Super-Ultra-Mega-Big 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 polygon-shaped 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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