SAT Math 2.4 Geometry and Measurement

Additional Topics in Math | Circles in the coordinate plane |

Area and Volume | Area |

Data Analysis | Geometric Probability |

Geometry | Area and Volume |

Language | English Language |

Math | Statistics and Probability |

Product Type | SAT Math |

SAT Math | Geometry and Measurement |

Statistics and Probability | Probability |

Okay, we’ve got this gray area – the circle, and…everything else.

We want to know the area of that circle compared to the area that isn’t inside the circle.

The easy peasy way is to figure out the area of the trapezoid,

figure out the area of the circle, and then divide the latter by the former.

Let’s start with the circle, because it looks… well, easier.

The formula for the area of a circle is pi r squared.

We know the circle has a diameter of 8, making the radius 4.

So… pi times 4 squared, or pi times 16… is roughly 50.24.

Moving on. Trapezoid time.

The area of a trapezoid is slightly more complicated…

One-half of base 1 plus base 2…times height.

Our top base is 8…

...but it seems the problem doesn't want to be as generous when it comes to the bottom base.

What if we make that right portion of the trapezoid into a triangle?

We get a triangle with a side of 8 and a hypotenuse of 10.

Well, hey – we recognize that sucker! It’s a classic 3-4-5 triangle…

meaning that the legs and hypotenuse have measurements that are multiples of 3, 4 and 5.

8 is double 4 and 10 is double 5…

...we have to double 3 to get the length of the remaining leg.

Which is 6.

So this leg is 6…plus 8…gives us a grand total of 14 for the bottom base.

Now we can plug into our trapezoid formula:

1/2 times 8 plus 14, or 22, times our height of 8…gives us 88.

Now don’t forget we have to divide the area of the circle by the area of the trapezoid.

So we have 50.24 divided by 88 gives us right around 57 percent… answer D.

All right, crisis averted.

Caitlin has been captured and strapped down.

We may now all enjoy the rest of our picnic.