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SAT Math 2.4 Geometry and Measurement

Language:
English Language

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...

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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