# Video: Finding the Perimeter of a Triangle using Properties of Parallelograms

Given that π΄π΅πΆπ· is a parallelogram and πΆπ = 8.6 cm, find the perimeter of β³π΄π΅πΆ.

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### Video Transcript

Given that π΄π΅πΆπ· is a parallelogram and πΆπ equals 8.6 centimeters, find the perimeter of triangle π΄π΅πΆ.

So here we have our parallelogram π΄π΅πΆπ·. And weβre told that πΆπ equals 8.6 centimeters. So letβs fill that into the diagram. Weβre asked to work out the perimeter of triangle π΄π΅πΆ. We can recall that the perimeter of a shape is the sum of the outside edge lengths. In other words, itβs the distance around the outside edges. So to work out the perimeter of our orange triangle, triangle π΄π΅πΆ, we can see that we are missing a few lengths. Weβre missing the length π΄π and the length π΅πΆ.

Letβs see if we can use any of the facts that we know about parallelograms to help us find these missing lengths. We can remember that opposite sides of a parallelogram are parallel and congruent. So now we know that our opposite sides are the same lengths. We know that our side length πΆπ· is 10 centimeters and also that our side π΅πΆ must be 11 centimeters. So now, if we look at our length π΄π, which is part of the diagonal π΄πΆ, we can use the fact that the diagonals of a parallelogram bisect each other. As they bisect each other, this means that the two parts of each diagonal are the same length. So our length π·π is equal to our length ππ΅. And importantly for us here, we now know that the length πΆπ is equal to the length π΄π, giving us that our final missing length is 8.6 centimeters.

So to find our perimeter of triangle π΄π΅πΆ, we add these lengths together. Which is 8.6 plus 8.6 plus 10 plus 11, simplifying to 38.2 centimeters. Which is our final answer for the perimeter of triangle π΄π΅πΆ.