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Application of Area of Parallelogram

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Explanation:

 

Parallelogram

Parallelogram


This parallelogram is a rhomboid as its angles are oblique.

Type

quadrilateral

Edges and vertices

4

Symmetry group

C2, [2]+, (22)

Area

B × H;
ab sin θ

Properties

convex

 

In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. In Euclidean Geometry, the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The three-dimensional counterpart of a parallelogram is a parallelepiped.

 

Area formulas

 

The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram

§  The area 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 rectangle is

and the area of a single orange triangle is

 

Therefore, the area of the parallelogram is

 

(Our solved example in mathguru.com uses this concept)

 

 

http://en.wikipedia.org/wiki/Parallelogram

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.