Question

What is the area of a rhombus?

Answer 1

Half the product of the length of the two diagonals.

Explanation:

The area of a rhombus is half of the enclosing rectangle.

The area of the rectangle is the product of the lengths of the two diagonals of the rhombus.

Answer 2

Divide the rhombus into two triangles, then solve for area.

Explanation:

In the image below, we can break the rhombus ABCD into two triangles, BAD and BCD. Then, we can solve the area of one of the triangles, then multiply by 2 to account for both.

`A=1/2 bh`

Triangle BCD has a height of 20, but we do not know the base. However, we can break BCD into two right triangles. Then we use the Pythagorean Theorum to figure out that line BO is about 22. 22*2 gives us the base of the triangle, because there are two right triangles with the base of 22.

Now we can calculate for the area of one of the triangles.

`A=1/2 (20*22)`
`A=220`

Then, we have to multiply by two to give us the area of the rhombus, because there are two triangles.

`A=440`