ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Area and Volume Videos 38 videos
Los cubos de hielo no son ruidosos generalmente...pero tienen un volumen de tipo diferente. Este video te enseñará cómo encontrar el volumen de...
Volume is crucial to our lives. It determines the amount of food we eat, the amount of fluid we drink, and hydraulics, just to to name a few. One o...
Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?
SAT Math 2.4 Geometry and Measurement 555 Views
Share It!
Description:
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.
Related Videos
SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?
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...
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...