Math Forum - Problems Library - Geometry - Quadrilaterals

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Geometry
  lines/angles
  triangles
  quadrilaterals
  polygons
  circles
  perimeter, area,
    volume
  similar/congruent
  right triangles
  transform/symmetry
  construction/locus
  coordinate geometry
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Geometry
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Quadrilaterals
Problems in this category incorporate the distinctions among different quadrilaterals. The solutions to some of the problems will require an algebraic equation supported by the properties of a specific quadrilateral. Others will require a determination of the type of quadrilateral that satisfies a given set of properties. Many of the problems in this category will require more advanced knowledge and integration of several geometric topics.

Related Resources
Interactive resources from our Math Tools project:
   Geometry: Quadrilaterals
The closest match in our Ask Dr. Math archives:
   Quadrilateral Classification
NCTM Standards:
   Geometry Standard for Grades 9-12


Access to these problems requires a Membership.

Area of a Rhombus - Annie Fetter
Geometry, difficulty level 2. Find the area of a rhombus, given one angle measure and the length of the longer diagonal. ... more>>

Arranging Rectangles - Annie Fetter
Geometry, difficulty level 3. Help Kasim decide if his arrangement of rectangles could ever form a square. ... more>>

Congruent Rectangles Help - Annie Fetter
Geometry, difficulty level 2. Find some possible areas for the large rectangle shown in the given picture. ... more>>

The Coordinated Quadrilateral - Annie Fetter
Geometry, difficulty level 3. A quadrilateral has vertices at (-3,6), (-1,-2), (7,-4), and (5,4). What kind of quadrilateral is it? ... more>>

Counting Squares - Annie Fetter
Geometry, difficulty level 2. Count the total number of squares in the given diagram. ... more>>

Drawing a Kite Plan - Annie Fetter
Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section. ... more>>

Finding FAB - Annie Fetter
Geometry, difficulty level 2. The measure of one angle in the given picture is x. Using your knowledge of rhombii and triangles (and other things!), find the measure of another angle. ... more>>

Finding the Base of a Trapezoid - Annie Fetter
Geometry, difficulty level 3. Given trapezoid ABCD, with AD one base and BC the other and a 60 degree angle at CDA. If CD is 26sqrt3/3 meters, BC is 7 meters, and the area of the trapezoid is 130 square meters, what's the length of AD? ... more>>

Four Point Puzzle - Annie Fetter
Geometry, difficulty level 3. The vertices of quadrilateral ABCD are at the points A:(1,2), B:(2,-2), C:(-5,-4), and D(-6,0). What's the most specific name you can give to this quadrilateral? ... more>>

Make a Square! - Annie Fetter
Geometry, difficulty level 3. Make two cuts in the given figure and rearrange the pieces to make a square. ... more>>

Name This Quadrilateral! - Annie Fetter
Geometry, difficulty level 3. A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides congruent, the other pair not congruent, and a pair of opposite angles that are supplementary. What is this figure, and how do you know? ... more>>

One Last Bit of Fun - Annie Fetter
Geometry, difficulty level 3. In parallelogram ABCD, the bisector of angle ABC intersects AD at P. If PD=5, BP=6, and CP=6, what is the value of AB? ... more>>

Overlapping Squares - Annie Fetter
Geometry, difficulty level 3. Two squares, one 8 cm on a side and the other 10 cm, overlap. A corner of the 10 cm square is anchored at the middle of the 8 cm square and can rotate around that point. What are the maximum and minimum areas they'll overlap? ... more>>

A Parallelogram Dissection - Annie Fetter and Everyday Math Grade 3
Geometry, difficulty level 3. Cut the given parallelogram along the dotted lines and rearrange the three resulting triangles to form what seems to be a square. What needs to be true of the original figure in order for the resulting figure to actually be a square? ... more>>

The Puzzling Parallelogram - Annie Fetter
Geometry, difficulty level 3. Draw a parallelogram ABCD with AB=10. Draw EF with E between A and B and F between C and D such that EF divides the area of ABCD in half. If EF=4, what is FD? ... more>>

Quad Query - Annie Fetter
Geometry, difficulty level 2. Given quadrilateral ABCD, with E the midpoint of AB and F the midpoint of AD. The area of FAEC is 13. What's the area of ABCD? ... more>>

A Rectangle Dissection - Annie Fetter
Geometry, difficulty level 3. Cut the given rectangle into three pieces as indicated by the dashed lines. Rearrange the pieces to form a square, and explain why the resulting shape actually is a square. ... more>>

The Return of the Parallelogram II - Annie Fetter
Geometry, difficulty level 3. Draw a parallelogram ABCD with AB=10. Draw EF with E between A and B and F between C and D such that EF divides the area of ABCD in half. If EF=4, what is the area of the parallelogram? ... more>>

Sighting in a Rifle - Annie Fetter
Geometry, difficulty level 3. Analyze the given target of four shots, and tell me how far to move the scope on my rifle so that the group of shots will be centered around the bull's-eye. ... more>>

Slicing a Cube - Annie Fetter
Geometry, difficulty level 3. Given a cube with a surface area of 54 cm^2, find the perimeter of the square cross section and that of the largest rectangular cross section of that cube. ... more>>

Whodunnit? - Annie Fetter
Geometry, difficulty level 4. Determine which quadrilateral the witnesses saw running from the scene of the crime. ... more>>

World Series Snafu? - Annie Fetter
Geometry, difficulty level 2. Determine what's wrong with the "official" dimensions of "home plate" in baseball. ... more>>

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