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SAT Math 2.4 Geometry and Measurement 555 Views
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SAT Math 2.4 Geometry and Measurement
Transcript
- 00:02
Here’s your shmoop du jour, brought to you by lawn darts.
- 00:06
Because there’s just about nothing safer and more fun than hurling sharp projectiles across the back yard.
- 00:13
If Caitlin throws a lawn dart so that it lands inside the trapezoid, what is the approximate
- 00:18
probability that it will land inside the circle?
- 00:22
Here are the potential answers...
Full Transcript
- 00:26
Okay, we’ve got this gray area – the circle, and…everything else.
- 00:29
We want to know the area of that circle compared to the area that isn’t inside the circle.
- 00:34
The easy peasy way is to figure out the area of the trapezoid,
- 00:37
figure out the area of the circle, and then divide the latter by the former.
- 00:41
Let’s start with the circle, because it looks… well, easier.
- 00:44
The formula for the area of a circle is pi r squared.
- 00:47
We know the circle has a diameter of 8, making the radius 4.
- 00:51
So… pi times 4 squared, or pi times 16… is roughly 50.24.
- 00:57
Moving on. Trapezoid time.
- 00:59
The area of a trapezoid is slightly more complicated…
- 01:02
One-half of base 1 plus base 2…times height.
- 01:05
Our top base is 8…
- 01:06
...but it seems the problem doesn't want to be as generous when it comes to the bottom base.
- 01:10
What if we make that right portion of the trapezoid into a triangle?
- 01:14
We get a triangle with a side of 8 and a hypotenuse of 10.
- 01:17
Well, hey – we recognize that sucker! It’s a classic 3-4-5 triangle…
- 01:23
meaning that the legs and hypotenuse have measurements that are multiples of 3, 4 and 5.
- 01:27
8 is double 4 and 10 is double 5…
- 01:30
...we have to double 3 to get the length of the remaining leg.
- 01:34
Which is 6.
- 01:36
So this leg is 6…plus 8…gives us a grand total of 14 for the bottom base.
- 01:41
Now we can plug into our trapezoid formula:
- 01:45
1/2 times 8 plus 14, or 22, times our height of 8…gives us 88.
- 01:52
Now don’t forget we have to divide the area of the circle by the area of the trapezoid.
- 01:55
So we have 50.24 divided by 88 gives us right around 57 percent… answer D.
- 02:01
All right, crisis averted.
- 02:02
Caitlin has been captured and strapped down.
- 02:04
We may now all enjoy the rest of our picnic.
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