# ACT Math: A Challenging Arc Length & Sector Area Problem

One of our more popular posts involves Arc Lengths & Sector Areas for circles. With that in mind, we thought we’d give you a challenging problem (well, really two problems) involving this topic. Give it a try and then scroll down for the answer.

The circle below has its center at O and triangle AOB is equilateral with sides that are each 6 inches. 1.  What is the area, in square inches, of the shaded region?

A.  6π – 3√3
B.  9π – 3√3
C.  6π – 6√3
D.  6π – 9√3
E.  9π – 9√3

# ACT Math: Arc Lengths and Sector Areas

As you’re reviewing for the geometry problems that appear on the ACT Math test, one of the things you’ll want to go over is circles. There are many types of problems that can appear on the test involving circles. This post will review two of those: arc length and sector area.

You can find both arc length and sector area using formulas. Or you can take a more “common sense” approach using what you know about circumference and area. Let’s look at both of these concepts using the following problems.

A circle with its center at Point O has a radius of 12 cm. If ∠AOB has a measure of 60 degrees, what is the length of arc AB? A.  2π
B.  4π
C.  6π
D.  12π
E.  24π