### Video Transcript

Given that π΄π΅πΆπ· is a parallelogram and πΆπ equals 8.6 centimeters, find the perimeter of triangle π΄π΅πΆ.

So here we have our parallelogram π΄π΅πΆπ·. And weβre told that πΆπ equals 8.6 centimeters. So letβs fill that into the diagram. Weβre asked to work out the perimeter of triangle π΄π΅πΆ. We can recall that the perimeter of a shape is the sum of the outside edge lengths. In other words, itβs the distance around the outside edges. So to work out the perimeter of our orange triangle, triangle π΄π΅πΆ, we can see that we are missing a few lengths. Weβre missing the length π΄π and the length π΅πΆ.

Letβs 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 πΆπ· is 10 centimeters and also that our side π΅πΆ must be 11 centimeters. So now, if we look at our length π΄π, which is part of the diagonal π΄πΆ, 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 ππ΅. And importantly for us here, we now know that the length πΆπ 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΅πΆ, 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΅πΆ.