Exercise 21 Page 410

The polygon has three sides and is therefore a triangle. The formula for calculating the area of a triangle is: A=1/2bh. If the segments BF and FA are perpendicular to each other we can use them as our base and height. To confirm that these two segments are perpendicular, we will first find their slopes and then compare them to see if the slopes are negative reciprocals.

Confirming the Right Angle

We will start by finding BF's slope.

Let's now calculate FA's slope.

Two lines are perpendicular to each other if the product of their slopes is - 1. m_(BF)* m_(FA)=1*(- 1)=- 1 Here the product is -1. So, the lines are indeed perpendicular.

Calculating Leg Lengths

Let's use BF as base. We calculate its length using the Distance Formula.

Let's now calculate the length side FA, which is the height in the triangle.

Calculating the Area

Now that we have the base and the height, we have enough information to calculate the triangle's area.

We now know that the triangle's area is A=6square units.