Area of composite figure with parallelograms
About this video
The video finds the area of a figure made of two congruent rectangles and four congruent parallelograms. Each rectangle is 15 × 2 = 30, each parallelogram is base 15 × height 7 = 105, and the total is 4 × 105 + 2 × 30 = 480 square units.
You'll be able to
- find the area of a parallelogram using base times perpendicular height.
- use congruent shapes to avoid repeating work.
- find the area of a composite figure by adding its parts.
Key words
- congruent
- Exactly the same shape and size.
- parallelogram
- A four-sided shape with two pairs of parallel sides.
- height
- The straight-up (perpendicular) distance between the base and the opposite side, not the slanted side.
- composite figure
- A shape made by joining simpler shapes.
Transcript
- [Narrator] We're told the following figure is composed of four congruent parallelograms and two congruent rectangles. So we have one rectangle up there, one rectangle down here, and then we have one, two, three, four congruent parallelograms. What is the area of the shape?
Pause this video, have a go at this before we do this together. All right, now, let's do this together. So, we could start with the rectangles. So, for example, this rectangle up here, its area is going to be 15 times two, so that area is going to be 30, and that's the same as this rectangle down here, because they say that these two are congruent, so that also has an area of 30.
Next, we have to figure out the area of one of these parallelograms, and if we know that, we just have to say, "Well, that's going to be the same area "as these other four, they're all congruent," and what we could do here, let's look at this one, let's look at this one right here, because they gave us the height here, the height is seven, what is this width right over here?
Well, this width is going to be that same 15. It's 15. So, the area of this parallelogram is base times height, right over here, not this side length, remember, we want the height, which they gave us, is actually seven. So, what's 15 times seven? That's 70 plus 35, this area is 105, and so is this one, is 105, and this one is 105, and this one is 105.
So, the area of the entire shape, let's see, if I have four times 105, that's going to be 420, and then I'm going to add plus 30, plus 30, so plus 60 is going to get me to 480 units, units squared, whatever the units we are dealing with right over here, and we're done.
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