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CAHSEE Math 3.4 Measurement and Geometry 192 Views


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Description:

Measurement and Geometry Drill 3 Problem 4. Find the area of the shaded region.

Language:
English Language

Transcript

00:03

Here’s your shmoopy question du jour…

00:05

The Scissors Bandit has escaped from prison

00:08

and has been wreaking havoc, cutting shapes out of paper wherever he goes.

00:14

The figure below consists of two identical square sheets of paper with a circle cut out

00:18

of one and a triangle cut out of the other. 

00:20

If one side of one of the squares measures 4 cm, find the area of the shaded region.

00:27

If we work together, maybe we can bring this jerk to justice.

00:30

And here are the potential answers...

00:34

OK, so this question is testing our visualization skills…

00:38

…as well as our ability to take “net” areas…

00:41

…that is, we’ll get the areas of the squares and then subtract the areas of the shapes inside.

00:47

Following in the Bandit’s footsteps, in a sense.

00:50

The problem tells us that the sides here are each 4 centimeters.

00:54

So we can get the areas of the squares pretty quickly.

00:58

The formula is base times height… and boy do we use that formula a lot so be sure you know it cold.

01:07

Each square’s area is 16 square centimeters.

01:11

Now for the tricky part.

01:12

We have to calculate the area of the triangle and the circle and SUBTRACT those areas from

01:17

that of the square. Because we shmoop daily, we know the formulas

01:21

for the area of a triangle and a circle – that is… one half base times height…

01:27

…and pi r squared, respectively So… plugging in the triangle’s numbers

01:32

we have one half times the base of 4 times the height of 4 and we get… 8 square centimeters.

01:41

Then we do the same for the circle and we get pi times the quantity 2 squared or …4.

01:47

Note that the radius is half the diameter of 4.

01:50

So now we solve for the whole thing and we get the area of the squares, which is 32 MINUS

01:55

the 8 from the triangle, MINUS the 4 pi from the circle.

02:00

And that gives us 24 minus 4 pi or answer D.

02:03

We’ve solved his crime… now it’s time for him to do the time…

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