how to prove the formula for are of rhombus?

Answer 1

Which formula are you trying to prove? If you are trying to prove the one based on diagonals: (d1*d2)/2 then start by inscribing the rhombus in a rectangle. Then note that the rhombus has half the the area of the rectangle and the fact that the diagonals of the rhombus are the same as the width and height of the rectangle.

Answer 2

The easiest way is to divide the rhombus into two triangles. Each triangle has an area of 1/2 times one base times the height of the rhombus. Add the two triangles' areas together to get the area of the rhombus.

Answer 3

Join any 2 opposite corners of the rhombus to divide the rhombus into 2 triangles.
Diagonals of the rhombus bisect each other at 90 degree.
Formula for triangle = 1/2 base x altitude
Area of 1st triangle = 1/2 x 1st diagonal x 1/2 x 2nd diagonal
Area of 2nd triangle(the 2nd triangle is on the same base as the 1st triangle) = 1/2 x 1st diagonal x 1/2 x 2nd diagonal
Area of rhombus = Area of 1st triangle + Area of 2nd triangle
= (1/2 x 1st diagonal x 1/2 x 2nd diagonal) + (1/2 x 1st diagonal x 1/2 x 2nd diagonal)
= 1/4 x 1st diagonal x 2nd diagonal + 1/4 x 1st diagonal x 2nd diagonal
= 1/2 x 1st diagonal x 2nd diagonal
Hence, proved.

Answer 4

do you mean area....

If so... a rhombust is just a paralelagram... then you can just either use that area formula, or you can divide it in to triangles and prove it that way.

(or are you looking for an integral proof. )

Answer 5

If you know the generator function, you can calculate the area by integrating between upper and lower limits. Refer to calculus book for further assistance.

Answer 6

on a paper with a pen

Answer 7

base time height.