Sum of Exterior Angles

Determine the sum of the exterior angles in any polygon.

Same Area: Triangle & Square

Construct a triangle that always has the same area as a square.

Rhombus and Circular Pool

Find a way to build the largest circular pool in a rhombus-shaped backyard.

Triangle or Square

Dissect a triangle into four parts so that it can be rearranged into a square.

Increasing Area

If the area of a rectangle increases, how much does its length and width increase?

Folding Squares

Use the perimeter of a rectangle to determine the area of a square.

Biggie Size It (Square)

If the area of a square increases by a certain amount, how long is an edge of the original square?

Land Dispute

Help settle a dispute over land between Squaresville and Centerville.

Constructing Squares

Can you construct a square that has twice the area of another square?

Triangle in a Quadrilateral

Given the ratio of a quadrilateral’s length to width, find the ratio of the area of a special shaded region to the area of the quadrilateral.

Minimum Perimeters

Find the minimum perimeter for a rectangle with a given area.

Penning for Pony

What are the dimensions of the largest rectangular pen Ted can make for his pony?

Tripling Perimeter

Find the length and width of a rectangle.

Rectangular Percents

Compare a rectangle’s area when its length and width are changed.

Tri-Square Trios

Find pairs of triangular numbers whose sum is a square number.

Almost a Square

What rectangle can you form that is close in shape to a square?

Dividing Rectangles

Find the possible areas of a rectangle that is formed from a larger integral rectangle.

Rectangle Squares

Given the perimeter of a rectangle, find its area.

Water Stop

How far does Paul walk to get a drink of water?

Transforming Triangle

What is the perimeter of a rectangle formed from an equilateral triangle?

Two Squares

Explore the relationship between length and area.

Isosceles Trapezoid

Investigate properties of an isosceles trapezoid.

Equal Sides

Construct an equal-sided quadrilateral inside a trapezoid or other quadrilateral.

Double the Fun

Determine ways to double the dimensions of quadrilaterals.

Optimal Quadrilaterals

Determine the largest area of a quadrilateral for a given perimeter.

Mystery Quadrilaterals

Classify a quadrilateral by making measurements in a dynamic construction.

Quadrilaterals Inscribed Inside Quadrilaterals

Explore properties of quadrilaterals constructed using the midpoints of the sides of given quadrilaterals.

Diagonals of Quadrilaterals

Explore the properties of the diagonals of various quadrilaterals.

Constructing Quadrilaterals 1

Given two parallel lines, form various quadrilaterals.


Make a triangle from a quadrilateral without changing the area.