Math Help Forum: Area of rhombus

I am having problems doing the following (please have a look at the attached figure):

Find the area of a rhombus whose side is 15 cm long while one of the diagonals is 24 cm long. Here AD=15 cm & AC=24 cm.
(Hint: Find OD using Pythagoras theorem)

Thanks,

Ron

Hello rn5a

Originally Posted by rn5a

I am having problems doing the following (please have a look at the attached figure):

Find the area of a rhombus whose side is 15 cm long while one of the diagonals is 24 cm long. Here AD=15 cm & AC=24 cm.
(Hint: Find OD using Pythagoras theorem)

Thanks,

Ron

Following my answer to your previous post, the other way of finding the area of a rhombus is to use the formula:

Area of rhombus = product of the lengths of the diagonals

The reason this formula works is because the diagonals of a rhombus are perpendicular, thus dividing the rhombus into four right-angled triangles. The area of each triangle is base x height; when you multiply this by 4, you'll find that you get the formula above.

So, use the hint you're given to find OD (which is half the length of one of the diagonals), and then multiply it by the length of the other diagonal.

Grandad

Area of rhombus = product of the lengths of the diagonals

The reason this formula works is because the diagonals of a rhombus are perpendicular, thus dividing the rhombus into four right-angled triangles. The area of each triangle is base x height; when you multiply this by 4, you'll find that you get the formula above.

Sorry but I couldn't exactly understand the above which I have quoted.

base x height x 4 = 2 base x height

So how does the Area of rhombus = product of the lengths of the diagonals?

Thanks,

Ron

Grandad explained it already:

The reason this formula works is because the diagonals of a rhombus are perpendicular, thus dividing the rhombus into four right-angled triangles. The area of each triangle is base x height; when you multiply this by 4, you'll find that you get the formula above.

Hello rn5a

Originally Posted by rn5a

Sorry but I couldn't exactly understand the above which I have quoted.

base x height x 4 = 2 base x height

So how does the Area of rhombus = product of the lengths of the diagonals?

Thanks,

Ron

In your diagram, if the diagonals meet at , then the four triangles: are congruent, and each is right-angled at . The area of one of them, for example , is . So the area of the rhombus is .

But and . So the area of the rhombus the product of the diagonals.

Grandad