For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

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### Area of a Parallelogram

#### Related Links

- Area: The number of square units it encloses
- Area of a parallelogram = base × height

### Area of a Parallelogram

- height = 10 · 3 = 30
- Area = base · height
- Area = (10)(30)

- height = 20 · 2 = 40
- Area = base · height
- Area = (20)(40)

- height = 15 · 2 = 30
- Area = base · height
- Area = (15)(30)

- height = 35 - 3 = 32
- Area = base · height
- Area = (35)(32)

- height = 5 + 3 = 8
- Area = base · height
- Area = (5)(8)

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Area of a Parallelogram

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Area 0:06
- Definition of Area
- Area of a Parallelogram 2:00
- Area of a Parallelogram
- Extra Example 1: Find the Area of the Rectangle 4:30
- Extra Example 2: Find the Area of the Parallelogram 5:29
- Extra Example 3: Find the Area of the Parallelogram 7:22
- Extra Example 4: Find the Area of the Shaded Region 8:55

### Basic Math Online Course

### Transcription: 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 5 ^{2} 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

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