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2. Parallelogram - Wikipedia

   en.wikipedia.org/wiki/Parallelogram

   The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram. The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the ...

3. Area - Wikipedia

   en.wikipedia.org/wiki/Area

   If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: [2] A = bh (parallelogram). A parallelogram split into two equal triangles

4. Parallelogram law - Wikipedia

   en.wikipedia.org/wiki/Parallelogram_law

   Given a norm, one can evaluate both sides of the parallelogram law above. A remarkable fact is that if the parallelogram law holds, then the norm must arise in the usual way from some inner product. In particular, it holds for the -norm if and only if =, the so-called Euclidean norm or standard norm. [1] [2]

5. Signed area - Wikipedia

   en.wikipedia.org/wiki/Signed_area

   The propositions in Book I concern the properties of triangles and parallelograms, including for example that parallelograms with the same base and in the same parallels are equal and that any triangle with the same base and in the same parallels has half the area of these parallelograms, and a construction for a parallelogram of the same area ...

6. Varignon's theorem - Wikipedia

   en.wikipedia.org/wiki/Varignon's_theorem

   An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...

7. Hooper's paradox - Wikipedia

   en.wikipedia.org/wiki/Hooper's_paradox

   The length of the shorter side at the right angle measures 2 units in the original shape but only 1.8 units in the rectangle. This means, the real triangles of the original shape overlap in the rectangle. The overlapping area is a parallelogram, the diagonals and sides of which can be computed via the Pythagorean theorem.

8. Pappus's area theorem - Wikipedia

   en.wikipedia.org/wiki/Pappus's_area_theorem

   Pappus's area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. The theorem, which can also be thought of as a generalization of the Pythagorean theorem , is named after the Greek mathematician Pappus of Alexandria (4th century AD), who discovered it.

9. Quadrilateral - Wikipedia

   en.wikipedia.org/wiki/Quadrilateral

   The area of the Varignon parallelogram equals half the area of the original quadrilateral. This is true in convex, concave and crossed quadrilaterals provided the area of the latter is defined to be the difference of the areas of the two triangles it is composed of.