# Euclid's Muse

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# Search Results for “Parallelogram”

##### Area of a Parallelogram
This app allows you to compare areas of a parallelogram and a rectangle in order to discover the formula for the area of the parallelogram.

Tags: area, parallelogram

##### Parallelogram area
Points E, F, G, H are proportion p along line segments AB, BC, CD, DE respectively. How does the ratio of the shaded parallelogram to the area of ABCD depend on p?

Tags: parallelogram, area, proportion

##### Euclids Elements – Book 1 – Proposition 42
To construct, in a given rectilineal angle, a parallelogram equal to a given triangle. In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle

##### Pythagoras generalization
A generalization of the Pythagorean Theorem, known to the ancients. The purple parallelogram is the same area as the two blue ones combined. Can you see why Pythagoras is a special case of this theorem?

Tags: Pythagoras, triangle, parallelogram

##### Euclids Elements - Book 1 - Proposition 45
Creating a parallelogram equal to a given quadrilateral with a given angle.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle, Angle

##### Area of a Trapezoid
This app allows you to compare areas of an arbitrary trapezoid and a parallelogram in order to discover the formula for the area of the trapezoid.

Tags: area, trapezoid

##### Area of a Triangle
This app allows you to compare areas of an arbitrary triangle and a parallelogram in order to discover the formula for the area of the triangle.

Tags: area, triangle