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### Course: MAP Recommended Practice > Unit 24

Lesson 6: Decompose figures to find area# Decomposing shapes to find area: subtract

Lindsay finds the area of an irregular shape by decomposing it into 2 rectangles and subtracting the area of the rectangles. Created by Lindsay Spears.

## Want to join the conversation?

- Why didn't you just subtract 16 from 72?(21 votes)
- If you are referring to2:22when she subtracts the 10 and then the 6, it is the same thing as subtracting 16. I believe she is just trying to break it down to make it simpler.(1 vote)

- Why does she say the area looks like a rectangle when it looks like a square?(4 votes)
- All squares are rectangles, but not all rectangles are squares. You can say that a square is a rectangle and be correct, but the inverse is not true, only some rectangles are squares.(4 votes)

## Video transcript

- [Voiceover] What is the
area of the shaded figure? So down here we have
this green shaded figure, and it looks like a rectangle
except it has a square cut out in the middle. So when we find its
area, we can think of it exactly like that. We want to know how much space it covers. It covers this rectangle's amount of area with this square cut out. So what we can do is find the
area of the larger rectangle and then cut out or subtract
the area of the square to see what's left in this shaded area. So let's start by finding the area of this larger rectangle. And to do that, we can
look at the side lengths. It has side lengths of nine and eight. To find the area of a
rectangle, we can multiple the side lengths. So nine times eight is 72. So that means that this rectangle covers 72 square centimeters. This entire rectangular area
covers 72 square centimeters. But now we need to cut out or subtract the area of this square
'cause that's not part of our shaded figure. We need to cut that part out. So to do that, we know
the side lengths are four on the square so we can think of this as this is four centimeters
across so we can divide it into four equal sections, and same going this way, and then if we connect these lines, what it will show us is that we have, it's not drawn perfect,
but we have four rows of four square centimeters. Four times we see four square centimeters. This top row, one, two,
three, four, and so on. Four rows, so there's
16 square centimeters we need to cut out of the 72 of this entire rectangular area, we need to cut out or subtract 16 of these square centimeters. So let's do that. We have 72 as the entire area, and then let's start subtracting out. We subtract out 10 of them, just for me like subtracting
10s 'cause they're simpler. So four, eight, 10 of
the square centimeters. Now we're down an area of 62 left. And then let's subtract those two more. We'll get us to subtract
two more, will get us to 60. And then there's four
left to subtract in order to subtract all 16, so 60 minus four gets us to 56. So the entire area of 72, we subtracted out these
16 square centimeters, leaves us with a final area of 56 square centimeters.