subject: Parallelogram Formula [print this page] The parallelogram is a quadrilateral in which the both pairs of the opposite sides are parallel. Then the opposite sides of the parallelogram are equal and the parallelogram diagonals bisect to each other.
Parallelogram which is having a pair of the adjacent sides are equal is known as rhombus. Parallelograms with a pair of adjacent sides are equal and one angle of a right angle is called a square.
Parallelograms Formula and Concepts:
Parallelogram formulae:
1. Formula of perimeter of a parallelogram:
P = 2S1 + 2S2
2. Formula of area of a parallelogram :
S = S2.height = S1 * S2 * sin A
3. Formula to find diagonals and sides of a parallelogram :
Diagonal12 + Diagonal22 = 2(S12 + S22)
4. The sum of two contiguous angles is 180:
A + B = 180 and A + D = 180
Concepts:
The opposite sides of the parallelogram are always equal in length.
The opposite angles in the parallelogram are always congruent.
The diagonals always bisect each other in the parallelogram.
Adjacent sides of a parallelogram are supplementary and their measures are add up to 180 degrees.
A parallelogram in which pair of adjacent sides are equal is called a rhombus.
A parallelogram with one angle a right angle is called a rectangle.
Reverse factors of a parallelogram are similar (by definition) and so will never meet.
The place of a parallelogram is twice the place of a triangular designed by one of its diagonals.
The place of a parallelogram is also similar to the scale of the vector combination item of two nearby factors.
Any range through the midpoint of a parallelogram bisects the place.[3]
Any non-degenerate affine modification requires a parallelogram to another parallelogram.
A parallelogram has spinning balance of purchase 2 (through 180). If it also has two collections of reflectional balance then it must be a rhombus or an rectangular.
The edge of a parallelogram is 2(a + b) where a and b are the measures of nearby factors.
Examples Using Parallelogram Formula's:
1. Find the area of a parallelogram with a height of 5 centimeters and a base of 20 centimeters.
Solution : Area of a parallelogram formula
Area = S2.height
Here from the given the S2 =20 and the height = 5
Plug these values in the above formula, we get
Area = 20 * 5 = 100 square cm
Therefore the Area of the parallelogram is 100 square cm.
2. Find the perimeter of a parallelogram with a side of 5 centimeters and 3 centimeters.
Solution :Perimeter of a parallelogram
P = 2S1 + 2S2
From the given, the side S1 = 5 and the side S2 = 3
Plug the above values in the formula, we get
P = 2 (5) + 2 (3)
P = 2 (5 + 3)
P = 2 (8)
P = 16 cm
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Therefore the perimeter of the parallelogram is 16 cm.
3. Find the perimeter of a parallelogram with a side of 10 centimeters and 3 centimeters.
Solution : Perimeter of a parallelogram
P = 2S1 + 2S2
From the given, the side S1 = 10 and the side S2 = 3
Plug the above values in the formula, we get
P = 2 (10) + 2 (3)
p = 2 (10 + 3)
p = 2 (13)
p = 26 cm
Therefore the perimeter of the parallelogram is 26 cm.
