Hmm

[The Preacher]

Find the area of a rhombus with sides 13 in. and one diagonal 10 in. long.

A rhombus is an equilateral parallelogram, so wouldn't it just be 13 x 13? I mean, all the sides are equal. Either way, that's not working for me. I'm learning about finding the area of triangles and stuff, but I don't know where to start on this one. Triangles are mean to me. I appreciate y'all's help.

 

[stapel]

It's a parallelogram, yes, but not a rectangle.

Eliz.

 

[The Preacher]

It's a parallelogram, yes, but not a rectangle.

Eliz.

Mmkay. So I need to find the area of the parallelogram that's not a rectangle.

I'm told that the area of a parallelogram is the product of any base and the altitude to that base. So I've got to multiply 13 by something.

I'm assuming that the diagonal that's 10 in. long is going to help me find the altitude. How do I use this diagonal, then?

EDIT: Do I need to find the other diagonal too?

 

[soroban]

Hello, Preacher!

Find the area of a rhombus with sides 13 in. and one diagonal 10 in. long.

           A*-----------*B
           / *5      * /
        13/   *   *12 /
         /     *     /   
        /   *12 *5  /
       / *       * /
     D*-----------*C

Did you know that the diagonals of a rhombus are perpendicular?

From the right triangles in the diagram,
\(\displaystyle \;\;\)we can find the length of the other diagonal (24).

Then triangles ABD and BCD have base = 24 and height = 5.
So we can find the area of the entire rhombus, right?

 

[The Preacher]

Hello, Preacher!

Find the area of a rhombus with sides 13 in. and one diagonal 10 in. long.

           A*-----------*B
           / *5      * /
        13/   *   *12 /
         /     *     /   
        /   *12 *5  /
       / *       * /
     D*-----------*C

Did you know that the diagonals of a rhombus are perpendicular?

From the right triangles in the diagram,
\(\displaystyle \;\;\)we can find the length of the other diagonal (24).

Then triangles ABD and BCD have base = 24 and height = 5.
So we can find the area of the entire rhombus, right?

Yes, thank you very much!

What's the formula for finding the distance between the right angle and the hypotenuse in a right triangle? In other words, I'm looking for how you found the other diagonal. Thanks, soroban.

 

[stapel]

I'm told that the area of a parallelogram is the product of any base and the altitude to that base.

Yes: the product of the base and the altitude, not the product of the base and the side. The product of the base and the side only work when the side is itself perpendicular to the base; that is, if the parallelogram is a rectangle.

Eliz.

 

[The Preacher]

I'm told that the area of a parallelogram is the product of any base and the altitude to that base.

Yes: the product of the base and the altitude, not the product of the base and the side. The product of the base and the side only work when the side is itself perpendicular to the base; that is, if the parallelogram is a rectangle.

Eliz.

Yes, you brought my attention to my error. I was agreeing with you, I know the difference between an altitude and a side (though, like you said, if the sides are perpendicular then they can be altitudes). I just got my formulas mixed up.

=]

 

[TchrQbic]

Hello, Preacher!

we can find the length of the other diagonal (24).

Then triangles ABD and BCD have base = 24 and height = 5.

What's the formula for finding the distance between the right angle and the hypotenuse in a right triangle? In other words, I'm looking for how you found the other diagonal.

The formula is our good friend, the Pythagorean theorem. We have the rhombus divided into four right triangles. We know the sides of the rhombus (hypotenuses for the right triangles) = 13. We know that the short leg of each right triangle = 5. Calling the long leg of each right triangle x, we can use 13² = 5² + x². That works out to 12.

 

[The Preacher]

Hello, Preacher!

we can find the length of the other diagonal (24).

Then triangles ABD and BCD have base = 24 and height = 5.

What's the formula for finding the distance between the right angle and the hypotenuse in a right triangle? In other words, I'm looking for how you found the other diagonal.

The formula is our good friend, the Pythagorean theorem. We have the rhombus divided into four right triangles. We know the sides of the rhombus (hypotenuses for the right triangles) = 13. We know that the short leg of each right triangle = 5. Calling the long leg of each right triangle x, we can use 13² = 5² + x². That works out to 12.

Oh, okay. Thanks, TchrQbic. =]