Finding Area of rhombus: perim = 100, diagonal = 30

[clb393]

Instructions: Find the area of each figure.
Problem: A rhombus has a perimeter of 100 meters and a diagonal 30 meters long. Find the area of the rhombus.

Ok so how do you find the area if you find the area if all you are given is the perimeter and an diameter of a rhombus? :?:

 

[Mrspi]

Re: Finding Area

Instructions: Find the area of each figure.
Problem: A rhombus has a perimeter of 100 meters and a diagonal 30 meters long. Find the area of the rhombus.

Ok so how do you find the area if you find the area if all you are given is the perimeter and an diameter of a rhombus? :?:

I suggest that you START by drawing a diagram, showing a rhombus with both of its diagonals.

Then, use some facts about a rhombus to help you fill in dimensions for the segments in the diagram.

All four sides of a rhombus are equal in length. If the perimeter is 100 m, then how long is each of the four sides?

You know that one diagonal has a length of 30 m. The diagonals of a rhombus BISECT each other, so the diagonal with length 30 m is divided into two equal parts by the other diagonal....how long is each of these parts?

Let the length of the "unknown" diagonal be 2x....it is divided into two equal parts by the known diagonal. How long is each of these parts?

Finally, the diagonals of a rhombus are perpendicular, so the four triangles formed by the two diagonals are right triangles.

You should be able to use the Pythagorean theorem to find the missing segment lengths.

When you've found the missing segment lengths, you will be able to find the area of each of those four right triangles...they're congruent triangles, they'll all have the same area. And the sum of the areas of those triangles will be the area of the rhombus.

 

[Loren]

Re: Finding Area

You need to read more carefully. A rhombus doesn't have a diameter.
The diagonas of a rhombus intersect at right angles and bisect each other.
Think, Pythagorean Theorem.
Furthermore, the area of a rhombus can be given as A=(1/2)d[sub:3gugsb40]1[/sub:3gugsb40]d[sub:3gugsb40]2[/sub:3gugsb40] where d[sub:3gugsb40]1[/sub:3gugsb40] and d[sub:3gugsb40]2[/sub:3gugsb40] are the measures of the diagonals.

 

[clb393]

Re: Finding Area

Instructions: Find the area of each figure.
Problem: A rhombus has a perimeter of 100 meters and a diagonal 30 meters long. Find the area of the rhombus.

Ok so how do you find the area if you find the area if all you are given is the perimeter and an diameter of a rhombus? :?:

I suggest that you START by drawing a diagram, showing a rhombus with both of its diagonals.

Then, use some facts about a rhombus to help you fill in dimensions for the segments in the diagram.

All four sides of a rhombus are equal in length. If the perimeter is 100 m, then how long is each of the four sides?

You know that one diagonal has a length of 30 m. The diagonals of a rhombus BISECT each other, so the diagonal with length 30 m is divided into two equal parts by the other diagonal....how long is each of these parts?

Let the length of the "unknown" diagonal be 2x....it is divided into two equal parts by the known diagonal. How long is each of these parts?

Finally, the diagonals of a rhombus are perpendicular, so the four triangles formed by the two diagonals are right triangles.

You should be able to use the Pythagorean theorem to find the missing segment lengths.

When you've found the missing segment lengths, you will be able to find the area of each of those four right triangles...they're congruent triangles, they'll all have the same area. And the sum of the areas of those triangles will be the area of the rhombus.

Thanks for the help, Mrspi! I forgot the rhombus had equal sides.