Finding AREA for Rectangles and Parallelograms
Rectangles!
In our class, we can find the area of a rectangle, but first we have to define what a rectangle is. I'm sure most of you can draw a rectangle, and that's fantastic! But let's make a definition for rectangle.
Rectangle - Noun - A closed 2D shape that has two sets of parallel lines, and four right angles.
The picture to the side shows us many rectangles. Now, I know what you're thinking. Ms. Heider, there's a square in that picture! You're right, my friend. There is a square in my picture. That's because a square is a type of rectangle.
Rectangle - Noun - A closed 2D shape that has two sets of parallel lines, and four right angles.
The picture to the side shows us many rectangles. Now, I know what you're thinking. Ms. Heider, there's a square in that picture! You're right, my friend. There is a square in my picture. That's because a square is a type of rectangle.
Now that we've figured out what a rectangle is, we can look at our formula for finding the area of our rectangle. The formula is:
AREA = BASE x HEIGHT (A = B x H)
Now we have some new words to define. Base and height are going to come up again and again as we work through some problems. So let's define what those are.
BASE is tricky, because any one of the sides can be our base! Let's look at a rectangle for an example. (Look to your SIDE to see the picture for base
AREA = BASE x HEIGHT (A = B x H)
Now we have some new words to define. Base and height are going to come up again and again as we work through some problems. So let's define what those are.
BASE is tricky, because any one of the sides can be our base! Let's look at a rectangle for an example. (Look to your SIDE to see the picture for base
HEIGHT is also tricky. When we think of height, we often think of how tall someone is, but in math, we define height a little bit differently. In math, height is measured by looking at the place where the line meets the base at a right angle and goes to the opposite vertex. (The vertices are those angles we see, like the corners in the rectangle picture. )
So now that we know what height and base are, we can figure out how our formula works.
We need to use multiplication to complete our problem. If we put numbers to our sides, then we can figure out our area. Our formula tells us that the PINK line, the BASE, multiplied by the BLUE line, the HEIGHT equals the area. To the side, you will find that I've added some numbers to our rectangle. Now we can find out how many square centimeters our rectangle is.
We know our base is 10 centimeters, and our height is 5 centimeters. That means that our AREA is 10 centimeters multiplied by 5 centimeters: A= 10 x 5
So if we multiply ten by five, we get 50 square centimeters!
We need to use multiplication to complete our problem. If we put numbers to our sides, then we can figure out our area. Our formula tells us that the PINK line, the BASE, multiplied by the BLUE line, the HEIGHT equals the area. To the side, you will find that I've added some numbers to our rectangle. Now we can find out how many square centimeters our rectangle is.
We know our base is 10 centimeters, and our height is 5 centimeters. That means that our AREA is 10 centimeters multiplied by 5 centimeters: A= 10 x 5
So if we multiply ten by five, we get 50 square centimeters!
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Watch the video to the side to practice another area problem for rectangles. Make sure you PAUSE the video before you see the answer so that you have a chance to try our strategies on your own. Remember, mathematics is about learning strategies and helping you develop your "math mind." It's not about getting the answer.
Were you able to get to the same answer as I did? Can you explain this answer to a friend? If you can, that's great! If not, try to watch the video again, this time follow along with me step by step. (If you're having a hard time seeing the colors, click the "watch on Youtube button!) |
Parallelograms!
Alright friends! Now we know how to find the area of a rectangle. Let's see if we can find the area of a parallelogram! Our first step is to define what a parallelogram is. There are lots of parallelograms! The picture to the side is one example of a parallelogram, but I'm sure we'll find many more.
A parallelogram is a 2D closed shape with four sides. It has two sets of parallel lines, just like a rectangle does! It also has two sets of matching (or congruent) angles. (Yes, this means that rectangles are parallelograms too!)
Most of the time in math class we will come across parallelograms that look similar to the one above. Since this shape has diagonal lines, we can't just immediately use our B x H formula to find area, but we CAN do this if we change our shape to being a rectangle. How can we change our shape? Well, we can cut and paste! Do you see any right triangles in our parallelogram? I do! This means that we can cut and move one of our right triangles so that we have a rectangle. Let's take a look at a picture to do that.
A parallelogram is a 2D closed shape with four sides. It has two sets of parallel lines, just like a rectangle does! It also has two sets of matching (or congruent) angles. (Yes, this means that rectangles are parallelograms too!)
Most of the time in math class we will come across parallelograms that look similar to the one above. Since this shape has diagonal lines, we can't just immediately use our B x H formula to find area, but we CAN do this if we change our shape to being a rectangle. How can we change our shape? Well, we can cut and paste! Do you see any right triangles in our parallelogram? I do! This means that we can cut and move one of our right triangles so that we have a rectangle. Let's take a look at a picture to do that.
The picture on the side shows a parallelogram on top. We've labeled our base and our height, but do you see the blue right triangle? Great! That means we can move the right triangle so that we can make a rectangle. Do you see where the blue triangle moved to? Now our parallelogram looks more like our "typical" rectangle. We know what to do from here! Remember our area for rectangles is BASE multiplied (or times) HEIGHT. Now we can solve for the area of a parallelogram, as long as move our right triangle first. Let's give it a try!
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As you watch the video, make sure you remember to PAUSE before I give the final answer, so that you can try it on your own. Remember, math isn't about finding the right answer, it's about learning strategies to solve problems. There's more than one way to look at the area of a parallelogram, this is just one way that works. When you're all finished with your problem, press play and see if you did end up with the correct answer. '
Can you explain why this answer is correct? |
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