Wednesday, May 15, 2013

Perimeter of a rhombus

Finding the perimeter of a rhombus

The video works out each problem

Perimeter of a rhombus

Let’s look at finding the perimeter of a rhombus. The perimeter is the distance around the outside of an object. A rhombus is similar to a square with a couple of unique features. They are both quadrilaterals but a rhombus doesn’t have right angles at the corners. Like a square a rhombus has congruent sides, so the perimeter formula is the same as a square, which is 4 times one side length.

Perimeter = 4s s=side

Problem 1. What is the perimeter of a rhombus with a side of 5 units?

perimeter of rhombus

 

 The video works the problem

Perimeter of a rhombus

Step 1. Use 4s

Step 2 4*5= 20 units Perimeter is linear, therefore it is not squared

Let’s next look at a problem a little more involved.

Find the perimeter of a rhombus with a diagonal of 10 units and measure of angle ABC equals 120 degrees.

 

 

Perimeter of a rhombus

Step 1. The diagonals  of a rhombus are  perpendicular to each other so they form right angles. These right angles  create a right triangle.

Step 2. The diagonal also bisects each other and divide each other in half. The 10 unit diagonal is divided into two 5 unit lines Combine step one and two  and you have a 30-60-90 right triangle  with a short leg of 5 units .

perimeter of a rhombus

 

 

 

Step 3. In order to find the side of the rhombus I will find the hypotenuse of the right triangle. The formula for the hypotenuse of a right triangle equals 2x

Step 4. We know x = 5 units from the diagonal being bisected by the other diagonal so it is 5 units.

So the hypotenuse equals 2*5 = 10 units

Step 5. Now use the perimeter formula of 4s which equals 4* 10 = 40 units