Video Transcript
𝐴𝐵𝐶𝐷 is a rectangle. Find the area of triangle
𝐴𝐵𝐹.
In the diagram, we can see that we
have a rectangle with vertices 𝐴, 𝐵, 𝐶, and 𝐷. However, we are interested in this
triangle 𝐴𝐵𝐹. That’s the triangle that has the
vertices 𝐴, 𝐵, and 𝐹.
Let’s recall the formula to find
the area of a triangle. The area of a triangle is equal to
one-half times the base times the height. And that height must be the
perpendicular height. But in this triangle, we don’t know
the perpendicular height, or do we?
We know that the rectangle has a
height of five centimeters. And since this is a rectangle, then
the distance from the base to the top will always be five centimeters. So the line segment 𝐴𝐵 is five
centimeters below 𝐹, which is the top of the triangle. We can show this on our diagram
with a line segment drawn from 𝐹 perpendicular to 𝐴𝐵.
So now we know that the triangle
has a base of eight centimeters and a perpendicular height of five centimeters. This means that the area of
triangle 𝐴𝐵𝐹 is one-half times eight times five. One-half of eight is four, and four
times five is 20. Not forgetting the units for the
area, we can give the answer that the area of triangle 𝐴𝐵𝐹 is 20 square
centimeters, since both of our lengths were given in centimeters.
