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Quadrilaterals
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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
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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.
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Angle Trisection with a Carpenter's Square
- Annie Fetter
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Geometry, difficulty level 3. Prove how a carpenter's square can be used to trisect an angle.
... more>>
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Area of a Rhombus
- Annie Fetter
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Geometry, difficulty level 2. Find the area of a rhombus, given one angle measure and the length of
the longer diagonal.
... more>>
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Checking a Building Foundation for Square
- Annie Fetter
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Geometry, difficulty level 2. How can you determine whether a rectangle is square when all you have is string and a tape measure?
... more>>
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Circle and Rhombus
- Annie Fetter
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Geometry, difficulty level 3. In the picture, we have a circle and a rhombus. BC is 6, AE is 4, angle DAE is 45 degrees, and AD is a diameter of the circle. How far is it around the perimeter of the whole figure?
... more>>
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The Coordinated Quadrilateral
- Annie Fetter
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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>>
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Counting Squares
- Annie Fetter
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Geometry, difficulty level 2. Count the total number of squares in the given diagram.
... more>>
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Drawing a Kite Plan
- Annie Fetter
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Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
... more>>
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Finding FAB
- Annie Fetter
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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.
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Finding the Base of a Trapezoid
- Annie Fetter
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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?
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Four Point Puzzle
- Annie Fetter
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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?
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Make a Square!
- Annie Fetter
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Geometry, difficulty level 3. Make two cuts in the given figure and rearrange the pieces to make a square.
... more>>
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Making a Quilt of Squares
- Annie Fetter
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Geometry, difficulty level 4. Figure out the dimensions of some closely packed squares.
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Name This Quadrilateral!
- Annie Fetter
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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?
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One Last Bit of Fun
- Annie Fetter
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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>>
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Overlapping Squares
- Annie Fetter
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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?
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A Parallelogram Dissection
- Annie Fetter and Everyday Math Grade 3
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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?
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The Puzzling Parallelogram
- Annie Fetter
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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?
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Quad Query
- Annie Fetter
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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?
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A Rectangle Dissection
- Annie Fetter
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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.
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The Return of the Parallelogram I
- Annie Fetter
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Geometry, difficulty level 3. Given parallelogram ABCD, with AB=10, and E on AB and F on CD. If EF is 4, what is the area of ABCD?
... more>>
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The Return of the Parallelogram II
- Annie Fetter
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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>>
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Sighting in a Rifle
- Annie Fetter
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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.
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Slicing a Cube
- Annie Fetter
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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.
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Splitting a Parallelogram
- Annie Fetter
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Geometry, difficulty level 3. Draw 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>>
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A Trapezoidal Garden
- Annie Fetter
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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>>
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World Series Snafu?
- Annie Fetter
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Geometry, difficulty level 2. Determine what's wrong with the "official" dimensions of "home plate" in baseball.
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