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Geometry and Measurement Videos 87 videos

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?

SAT Math 1.3 Geometry and Measurement
231 Views

SAT Math 1.3 Geometry and Measurement. Find the length of CE.

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SAT Math 2.4 Geometry and Measurement 555 Views


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Description:

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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