Area of a Parallelogram

The area of a parallelogram is base times height. But how did we arrive at this formula?

We discover two different ways of finding the area of a parallelogram by breaking it into rectangles and triangles.

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[mister_meatloaf]

One of the greatest facts about cheap internet is that it has made contents like these readily available for kids. Such a great way to unfold interest in this subject within kids.

[SwarnadruRoyChowdhury-yykl]

For a Rhombus
Area = ½ × one diagonal × another diagonal

[NavyaThareja-jtxp]

There are 2 ways
1/2 x diagonal 1 x diagonal 2

As rhombus is also a parallelogram,
Its area can also be( b x h )

[shadestheshadow]

Maybe split the rhombus into 2 triangles and combine the areas of said triangles

[aartisaxena]

Join any one diagonal of the rhombus...and we would get two congruent isosceles triangles....therefore, both of their areas will equal....and we would be able to find the area of the rhombus by adding the areas of both the triangles....

[THEPLAYERONEGAMING]

1/2* product of diagonals this is derived from Pythagorean theorum

[aayushrajesh]

Area of a rhombus= 1/2 d1*d2
a=(d1/2)(d2/2)
Where d1 is one diagonal
D2 is second diagonal

[kv]

4a if we adjust the tilted sides it'll look like square or else cut it into 4 pieces which is a right angle triangle then 4 x 1/2 bh will give area

[gitanjalideb]

Area of rhombus is 1/2 (ab) where a and b are the diagonal of the rhombus.

[santhiyagovindarajan]

Its area will be 24 sq units based on the diagram.
Join the opposite vertices you will get 4 right triangle with base= 3 and height = 4.
Hence area of rhombus = 4(1/2×3×4)= 24 sq units.

[MePatrick]

let the basis vectors of a matrix be the horizontal vector and the diagonal vector. The determinant of that matrix will exactly be the area of the parallelogram.

[geoarmstrong-mpqu]

split the triangle into 2 equal and symmetrical part .then, area of the rhombus=2*base*height

[penguincute]

A rhombus is a type of parallelogram so each of the opposites sides are parallel and we now have a parallelogram to calculate.

[rudrakumar]

We can divide it into into two from mid than can calculate the area of the triangle and then double it .

[VinsenTheCoolDude]

It's: Base × height as there's 2 triangles of the same size

[Handleoom]

I think for rhombus is ½×daigonal1×daigonal2 i guess

[leonemilianovillarinocarri]

We can cut the rombus into 2 triangles and gluing the triangles we have a parallelogram and using the two metods we can have the area

[MuSicBlock]

Let's split the rhombus into 4 triangles with the same measures. As you can see, each triangle has as height and width the half of the distances of two parallel vertices. So, half of 6 is 3 and half of 8 is 4. 3×4 equals 12, then you divide by two (the triangle is b×h÷2) which gives 6, then you multiply 6 by 4, that gives you 24. The area of the rhombus is 24.
24 is the half of 48, the area of a rectangle with the same width and height. Therefore, the formula of a rhombus is d1×d2 / 2.

[Yashir-ix]

Everyone should learn or formulae derivation these are important base for jee preparation.

Only for to be jee aspirant

[PixelPoineers]

Both are same, area of a rectangle is lxb and area of two same sized triangles is also bxh