Question Video: Finding the Area of a Triangle in a Given Rectangle Mathematics • 6th Grade

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.