Formula For Area Of Parallelogram

What is a Parallelogram?
Expanse of a Parallelogram
How to Discover the Area of a Parallelogram
Area of a Parallelogram Formula
Surface area of a Parallelogram Example

What is a Parallelogram?

Any shape with the word "parallel" in it gives abroad an important insight: the 4-sided shape will have two pairs of contrary, parallel sides.

As a quick refresher, a parallelogram is a plane figure, and then it is two-dimensional. It is a closed figure with straight sides, a blazon of quadrilateral (four-sided shape). Considering reverse sides are parallel, opposite angles and sides are congruent (the aforementioned).

$What is a Parallelogram?$

Three quadrilaterals, a rhomb, a foursquare, and a rectangle are specific types of parallelograms.

Suppose you congenital a crate to hold, say, oranges, but you forget to put a lesser on it. Two of the crate'southward sides are 12 inches and the other two are xviii inches. If you plough the crate and so i of its 18-inch sides is flat on a table, the crate naturally leans (considering information technology had no lesser to hold the iv sides rigid).

The leaning crate forms a parallelogram. If yous push or pull the crate and so it leans more or less, every shape it takes is a parallelogram. Its sides never change their length, merely the crate's height (or width) changes.

Surface area of a Parallelogram

If you noticed the three special parallelograms in the listing above, you already accept a sense of how to find area. Finding the surface area of a rectangle, for example, is like shooting fish in a barrel: length x width, or base x summit. The length of any linear geometric shape is the longer of its ii measurements; the longer side is its base.

For any parallelogram, nosotros need to know the length of a longer side (base of operations), and its width. This is where things go tricky, because the altitude along either short side is non necessarily its width. Call back of our wobbly orange crate; we could about collapse information technology flat, but its two short sides would always be 12 inches.

How to Find the Surface area of a Parallelogram

We can name the various parts of our orange-crate parallelogram. The four vertices (corners) are $A$ , $B$ , $C$ and $D$ . The two long sides, at eighteen inches, are $A B$ and $C D$ . Side $C D$ forms the base ( $b$ ) of our parallelogram.

$area of a parallelogram formula$

The 2 short sides, at 12 inches, are $B C$ and $D A$ . The width (or height) of the crate -- the altitude direct beyond from the base of operations to the other side -- could vary depending on the within angles of vertices $A$ , $B$ , $C$ and $D$ .

Nosotros need to discover the width (or height) $h$ of the parallelogram; that is, the altitude of a perpendicular line fatigued from base $C D$ to $A B$ .

Area of a Parallelogram Formula

If you know the length of base $b$ , and y'all know the height or width $h$ , you can now multiply those ii numbers to get area using this formula:

$a r e a = 18 i north \times 9 i northward$

Then, we get our answer:

$a r eastward a = 162 i n^{2}$

How to Calculate the Expanse of a Parallelogram

That calculation seems too uncomplicated and does not seem to take into account the angled sides, does information technology?

But consider, we can movement the parallelogram and modify its angles. At some point, we tin make every interior angle a right angle and get a rectangle. That means, no matter the angles we push button and pull the parallelogram into, the iv sides enclose the same area.

Some other way to call up of it is to consider cutting off a triangle from, say, the left side of the parallelogram to exit a nice, perpendicular corner. Move that cut off triangle over to the right side and the parallelogram is all of a sudden a rectangle. The surface area of a rectangle is easy, remember? Length x width in square units, which is the aforementioned as base of operations x height (b x h) in square units.

Expanse of a Parallelogram Example

A parallelogram has sides 35 cm and 17 cm, with a height of xi cm. What is its area?

$area of a parallelogram example$

Our formula:

$a r eastward a = b \times h$

Kickoff by plugging the base and peak into our formula

$a r e a = 35 c g \times xi c 1000$

Then, we multiply these two numbers together and become our answer:

$a r e a = 385 c {one thousand}^{2}$

Lesson Summary

We have reviewed what a parallelogram is, what its parts are, and how to notice its area, which is always expressed (written) in foursquare units. The parallelogram is a quadrilateral with reverse sides parallel; information technology e'er has four sides, and one longer side will ever exist its base.

To detect its surface area, y'all need to know its height. Multiply the length of the $b a s e \times h e i g h t$ , and express the answer in square units.

What you learned:

This lesson shows you lot how to find the area of whatever parallelogram, reviews the parallelogram's identify in geometry, and helps you identify key parts and measurements for finding the parallelogram's area.

After completing this lesson and studying the video, yous should be able to: