Perimeter of a Parallelogram
by Lily, Aug 02 2023
What is the Parallelogram
A parallelogram is a specific type of quadrilateral, which is a polygon with four sides. What sets a parallelogram apart is that opposite sides are parallel and congruent. In other words, it has two pairs of parallel sides.
Properties of a Parallelogram:
- The sides opposite to each other are of equal length (AB = DC).
- The angles facing each other are equal (angle D = angle B).
- If one angle is right (like 90 degrees), then all angles will be right angles.
- The diagonals of a parallelogram will cut each other in half. It's like drawing a line right in the middle!
- Both diagonals of a parallelogram divide it into two congruent (that means equal!) triangles.
Perimeter of Parallelogram
Now, let's tackle the perimeter of a parallelogram! To find it, we simply add up all the sides. It's like going on a treasure hunt to measure each side and then adding them up to get the magic number!
Formula for Perimeter of a Parallelogram:
If "a" and "b" are the sides of our parallelogram, then its perimeter (P) is given by:
P = 2(a + b)
Perimeter of a Parallelogram with Base(b) and Height(h)
Oh, but wait! There's another way to find the perimeter if we have the base (b) and height (h) of the parallelogram. Let's dive into it!
Perimeter with Base and Height:
If we have the base (b) and height (h) of the parallelogram, then its perimeter (P) is given by:
P = 2(b + h/cos θ)
Here, θ is a special angle between the height and the side of the parallelogram. It's like solving a puzzle to find that angle!
Problems with Solutions
Let's Test Our Skills with Fun Problems!
Unravel the mystery of another parallelogram whose base is 9 centimeters and the perimeter is 54 centimeters. Can you find the length of the other side?
Solution:
- Base, b = 9 centimeters
- Perimeter, P = 54 centimeters
- We know that the perimeter of a parallelogram is given by the formula: P = 2(a + b) units.
- Now, let's solve for "a" (the other side) using the given values in the formula:
54 = 2(a + 9)
54 = 2a + 18
2a = 54 - 18
2a = 36
a = 36/2
a = 18 centimeters
- Hooray! The length of the other side of the parallelogram is 18 centimeters.
Conclusion
Perimeter is like giving a big hug to a shape to measure its length all around. To find the perimeter, just add up all the sides. If "a" and "b" are the sides, the formula is P = 2(a + b). But wait, there's another way! If we know the base (b) and height (h), it's P = 2(b + h/cos θ), where θ is a special angle. Let's solve fun problems together! For example, a parallelogram with a base of 8 meters and side of 6 meters has a perimeter of 28 meters. Another one with a base of 9 centimeters and perimeter of 54 centimeters has the other side length of 18 centimeters. Happy exploring!