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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 912
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'seye.
... 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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