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Perimeter, Area, and Volume
The problems in this section explore the numerical and/or physical properties of perimeter, area, and/or volume, which are among the most important (and practical!) topics in a standard geometry curriculum. Some problems deal with classic geometric relations, but many incorporate practical applications. Heron's formula would be an appropriate search topic as a special subject.

Related Resources
Interactive resources from our Math Tools project:
   Geometry: Perimeter, Area, & Volume
The closest match in our Ask Dr. Math archives:
   High School: Euclidean/Plane Geometry
NCTM Standards:
   Geometry Standard for Grades 9-12

Access to these problems requires a Membership.

A Trapezoidal Garden - Annie Fetter
Geometry, difficulty level 2. Given trapezoid ABCD, with E on AD and F on BC and EF parallel to AB. If AE is 3/4 of ED, and BC is 14 feet, how long is FC? How does the area of DCFE compare to the area of EFBA? ... more>>

Triangles and String - Annie Fetter and Steve Risberg
Geometry, difficulty level 2. Given a loop of string 12" long, find all possible triangles of integer side lengths that it can form, and explain whether they are scalene, isosceles, or equilateral, as well as acute, right, or obtuse. ... more>>

Triangles, Area, and Congruence - Annie Fetter
Geometry, difficulty level 2. If two triangles have equal area, does that mean that they are congruent? ... more>>

Trisecting a Square - Annie Fetter
Geometry, difficulty level 2. Explain how to use the given method to trisect the area of a square. ... more>>

TV Dimensions - Annie Fetter
Geometry, difficulty level 2. If the aspect ratio of a TV is 16:9 and the diagonal measures 50 inches, what are the dimensions of the screen? ... more>>

Two Rectangles - Annie Fetter
Geometry, difficulty level 3. Given the area of one rectangle, find the area of the other rectangle in the picture. ... more>>

Unravelling the Mysteries of the Universe - Annie Fetter
Geometry, difficulty level 2. How many Earths can fit in Uranus? ... more>>

Waiting for Hot Water - Annie Fetter
Geometry, difficulty level 2. If a water pipe is 1/2" in diameter, the faucet is about 35 feet from the hot water tank, and the faucet runs at 3 gallons per minute, how long will it take the hot water in the tank to reach the faucet? ... more>>

The Water in My Pool - Leigh Nataro
Geometry, difficulty level 2. Based on one measurement taken from the edge of my circular pool, what is the volume of my pool? ... more>>

Well, Well, Well - Annie Fetter
Geometry, difficulty level 1. Figure out the diameter of my cousin Frank's new well. ... more>>

Which Pizza? - Annie Fetter
Geometry, difficulty level 2. Which is a better deal - a 16" diameter pizza for $11 or a 10" diameter pizza for $7? ... more>>

Winning at Biathlon - Annie Fetter
Geometry, difficulty level 3. Figure out which of two fictional biathletes will win a race. ... more>>

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