ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Statistics and Probability Videos 134 videos

SAT Math 1.2 Statistics and Probability
1060 Views

SAT Math: Statistics and Probability Drill 1, Problem 2. If the four largest numbers in the set were doubled, what would happen to the median...

SAT Math 1.4 Statistics and Probability
380 Views

SAT Math 1.4 Statistics and Probability. If two standard 6-sided dice are rolled, what is the probability that the sum of the dice will be gre...

SAT Math 1.5 Statistics and Probability
358 Views

SAT Math 1.5 Statistics and Probability. If Silas draws one card, then places it in his pocket and draws another, what is the probability that...

See All

SAT Math 2.4 Geometry and Measurement 555 Views


Share It!


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.

Related Videos

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math 9.4 Algebra and Functions
1300 Views

SAT Math 9.4 Algebra and Functions

SAT Math 9.2 Algebra and Functions
377 Views

SAT Math 9.2 Algebra and Functions

SAT Math: Identifying an Equation for the Average of Two Percentages
23 Views

In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...

SAT Math: Which Equation Represents Profit?
13 Views

Angela is making cookies for a bake sale. She expects each batch of her cookies to sell for $40. It costs her $10 to make one batch of cookies, and...