If a rectangular garden were 2 feet wider and 3 feet longer, it would
be 64 square feet larger. If it were 3 feet wider and 2 feet longer,
it would be 68 square feet larger. What are the dimensions of the
garden?

Geometry

6th to 8th, High School

A Line of Reflection
Find the equation of the line of reflection for triangle ABC and its
image, A'B'C'.

Geometry

6th to 8th, High School

A Minor Problem
A chord of a circle is one side of an equilateral triangle. The other
two sides of the triangle are radii of the circle. Find the length of
the minor arc subtended by the chord.

Geometry

6th to 8th, High School

A Parallelogram Dissection
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?

A Quickie Triangle Puzzle
Find the length of the unknown side of this triangle using knowledge
of special right triangles.

Geometry

6th to 8th, High School

A Rectangle Dissection
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.

A Tangent Square and Circle
The square and circle below are tangent at one point and meet at four
other points, as shown in the picture. If the side of the square is 8
units long, what's the radius of the circle?

Geometry

High School

A TriangleSquare Ratio
A square with side length s is inscribed in an equilateral triangle of
side length t. Find the ratio of (t/s), accurate to four places to
the right of the decimal.

Geometry

6th to 8th, High School

A Triangular Garden
Cynthia has two pieces of garden edging. One is 8' long and the other
is 6'. Will a third side of 12' or 11' make a triangle with a larger
area?

Geometry

6th to 8th, High School

Added Areas
A circle and an isosceles triangle are inscribed in a square. If the
areas of the three figures added together is 28 square units,
what's the edgelength of the square?

Geometry

6th to 8th, High School

All Around the World
If a wire wrapped around the equator of the Earth is lengthened, how
far above the surface of the Earth would the wire now be
if lifted off the surface an equal distance all the way around?

Geometry

6th to 8th, High School

An Inscribed Circle
A circle is inscribed in a triangle with sides of 6, 6, and 4. What's
the radius of the circle?

Geometry

6th to 8th, High School

Analyzing Angles
Given some information about angles in a picture, figure out some of
the angle measures.

Geometry

6th to 8th, High School

Another Ambiguous Angle
Given isosceles triangle ABC, with BE perpendicular to AD. If angle
ACB is x, what is angle CBE?

Geometry

6th to 8th, High School

Ants Marching
Traveling along the edges of a cross section of the cube, find the
length of the shortest possible path from one corner of a cube to the
opposite corner, as well as the longest possible path between the same
corners.

Geometry

6th to 8th, High School

Approximating Pi
Approximate the value of pi using polygons instead of a circle.