For the given diagram, we will find the area of the sector and then the area of the triangle. Finally, we will find their difference to find the area of the segment.
Area of the Sector
The area of a sector of a circle is the product of the measure of the arc divided by 360 and the area of the circle.
With this in mind, let's consider the given diagram.
We can see that the radius of the circle is 8ft. Also, the measure of the central angle that corresponds to our arc is 90. Recall that the measure of an arc is the same as the measure of its corresponding central angle. Therefore, the measure of our arc is also 90. Let's update our diagram.
We have all the information we need to calculate the area of the sector. Let's do it!
The area of a triangle can be found by taking half the product of two side lengths and the sine of the included angle. With this in mind, let's consider the triangle in our diagram.
The length of both of the known sides is 8ft and the included angle measures 90^(∘). This is enough information to find the area of the triangle.
