Basic Math Area of a Parallelogram

Welcome back to Educator.com.0000

For the next lesson, we are going to go over the area of a parallelogram.0002

First let's talk about area.0008

An area of a figure is the number of square units it encloses.0010

Another way to think of area is how much space it covers.0017

Let's say you have to cover your book.0023

That is all area because you are covering something.0028

It is how much space that you are covering.0031

If you have a hole in your jeans and you need to patch it up,0033

that is going to be area because it is the space that you are covering.0037

This, square units, it means how many 1 unit squares it covers.0044

This rectangle here, if I say that there are 8 square units,0055

that means each one of these squares, if it has a measure of 1 unit.0066

Units can be like centimeters, inches, whatever; this is 1; this is 1.0076

The area of this right here is 1 square unit.0081

How many square units is in this rectangle?--1, 2, 3, 4, 5, 6, 7, 8.0086

The area is 8 square units; it is how many square units it is covering.0092

If I say this is 1 inch, then this is 8 inches squared.0106

8 square units is 8 inches squared; that is area.0115

We know the area of a rectangle is base times height.0121

Area equals base times height.0125

A rectangle is a type of parallelogram; we learned that in the previous lesson.0129

A rectangle is a type of parallelogram; that formula applies to rectangles and to parallelograms.0133

Here this is a rectangle.0143

If this is the base, this is the height, we just multiply this side with side and we get the area.0145

We figure out how much space this is covering.0151

For parallelogram, if I maybe let's say I cut this whole part out.0157

This is the height; height always has to be perpendicular to the base.0169

This is the height; this is the base.0173

This whole thing is the base; height, base, perpendicular.0176

If I cut this piece out, say I am going to cut this out.0182

I take it over to this side; I glue it over here.0190

This is all going to be right here; then what do you get?0201

This part I cut out; then isn't this part a rectangle?0206

All this then becomes a rectangle; this is gone; this was moved over here.0213

A parallelogram covers the same amount of space as a rectangle.0226

So the formula is still the same.0231

Just make sure if you are going to find the area of a parallelogram,0232

you have to make sure that the height is perpendicular.0236

The height is from here to here; that is the height.0240

This right here cannot be the height.0245

It is like when you measure how tall you are,0248

if you measure your height, you have to be standing up straight.0250

You can't be slouching; you can't be leaning over to the side.0254

Same thing; the height of this parallelogram is not the side that is leaning over.0258

It has to be straight perpendicular; that is the height.0265

The first example, we are going to find the area of this rectangle.0273

We know it is a rectangle with four congruent sides, meaning four sides are the same.0276

That means this is actually a square; a square is a type of rectangle.0283

If this is 5, this is also 5.0289

The area is base times height which is 5² or 5 times 5.0294

We know that is 25; then units, centimeters.0307

For area, because we are looking at how much space it covers,0313

it is centimeters squared because we are looking at base and height, two dimensions.0317

The area of this is 25 centimeters squared.0324

Find the area of the parallelogram.0331

The first one, this is 9 inches, 7 inches, and 6 inches.0336

The area is base times height.0343

Again remember the height and the base, they have to be perpendicular.0347

If I want to measure how tall the height of this perpendicular, I can't measure thi8s.0352

I can't measure it this way.0357

I have to make sure I measure it perpendicular, straight up and down.0359

The base will be 9; the height is going to be 6.0366

The area is 54 inches squared.0374

The next one, same thing; this is a parallelogram with four congruent sides.0385

We know that this a rhombus; the area is base times height.0393

Let's see; what is the base?0405

Even though we know that that is 2, that has nothing to do with our base.0408

The base is from here to here; that is 10.0412

Our height, even though the height is given to you on the outside of it,0418

it still measures from top straight down, perpendicular.0422

The height is 8; the area becomes 80 meters squared.0428

The next example, the base of a parallelogram is 10 inches.0445

The height is twice the base; find the area of the parallelogram.0450

If I draw a parallelogram, say there is my parallelogram.0456

The base is 10 inches; the height is twice the base.0463

Make sure you don't label this the height; the height has to be perpendicular.0471

You can draw a dotted line like that; that is twice the base.0480

Twice means 2 times the base; double the length of the base.0486

This is 2 times 10 which is 20.0492

The base is 10; it is twice; 2 times bigger, then it is 20 inches.0498

Area of this parallelogram is base times height; the base is 10.0504

The height is 20; 10 times 20 is 200.0512

It is in inches; it is inches squared.0523

The final example, find the area of the shaded region; we have two rectangles here.0537

This is the big one; here is the smaller one that is inside.0546

We are just trying to find the area of just the blue part, the shaded part.0554

That means I need to do two things.0561

I have to find the area of both rectangles; then I have to do what?0566

It is like saying... let's say I have a piece of paper.0571

Let's say this big rectangle is the piece of paper.0574

If I find the area of that this big rectangle,0582

that is going to be the area of that piece of paper, the whole thing.0585

But then I cut a rectangle out of that paper; it becomes white.0589

How would I figure this out?0602

I need to find the area of the big rectangle.0605

That is going to be everything.0610

If I find the area of the big rectangle, it is going to be this whole thing.0611

That is our piece of paper.0616

If I cut out another rectangle piece right there like that,0618

don't I subtract it?--because it is no longer there.0625

This base right here is empty; it is not being covered.0629

You have to subtract it; subtract the small rectangle; you are cutting it out.0634

That is going to be the area of the shaded.0640

Again the whole thing, the area of the big one is going to be 20 times 9.0643

The base times the height; 20 times 9.0655

That is... 20 times 9; 2 times 9 is 18.0659

Then I can just add a 0 at the end of that.0665

That is how you multiply numbers.0667

If I have a 0 at the end of a number that I am multiplying,0668

then I can just put that 0 at the end of my answer.0672

It is 20 times 9; you can just do that too; 0 and then 18.0676

That is where that 0 comes from; meters squared.0681

That is the area of this big one.0688

I can't say that is my answer because remember you cut out that little piece.0691

This part is not covering anything; it is an open spot.0695

To find the area of this rectangle, this is the area of just the first one.0702

Let's say that is the first one.0710

The area of the second one is 10; the base is 10.0712

Times, the height is 3; the area is 30 meters squared.0721

This is the part that we cut out.0731

I have to subtract it because it was originally covering this much space.0734

But then I cut out this much; I have to subtract it.0740

My area of the shaded becomes then 150 meters squared.0745

That is it for this lesson; thank you for watching Educator.com.0760