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

π΄π΅πΆπ· is a rectangle. Find the area of β³π΄π΅πΉ.

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Video Transcript

π΄π΅πΆπ· is a rectangle. Find the area of triangle π΄π΅πΉ.

In the diagram, we can see that we have a rectangle with vertices π΄, π΅, πΆ, and π·. However, we are interested in this triangle π΄π΅πΉ. Thatβs the triangle that has the vertices π΄, π΅, and πΉ.

Letβ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 donβ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 π΄π΅ is five centimeters below πΉ, which is the top of the triangle. We can show this on our diagram with a line segment drawn from πΉ perpendicular to π΄π΅.

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 π΄π΅πΉ 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 π΄π΅πΉ is 20 square centimeters, since both of our lengths were given in centimeters.