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Course: Grade 7 (TX) > Unit 1
Lesson 5: Circles and composite figures- Relating diameter and circumference
- Area of composite figure with parallelograms
- Area of composite figure with circles
- Converting between measurement systems
- Convert between measurement systems
- Diameter and circumference patterns
- Relate diameter and circumference
- Area of a circle
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Area of composite figure with parallelograms
Find the area of a composite figure by splitting it into congruent parallelograms and rectangles. Created by Sal Khan.
Video 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.