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

Given that 𝐴𝐡𝐢𝐷 is a parallelogram and 𝐢𝑀 = 8.6 cm, find the perimeter of △𝐴𝐡𝐢.

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Video Transcript

Given that 𝐴𝐡𝐢𝐷 is a parallelogram and 𝐢𝑀 equals 8.6 centimeters, find the perimeter of triangle 𝐴𝐡𝐢.

So here we have our parallelogram 𝐴𝐡𝐢𝐷. And we’re told that 𝐢𝑀 equals 8.6 centimeters. So let’s fill that into the diagram. We’re asked to work out the perimeter of triangle 𝐴𝐡𝐢. We can recall that the perimeter of a shape is the sum of the outside edge lengths. In other words, it’s the distance around the outside edges. So to work out the perimeter of our orange triangle, triangle 𝐴𝐡𝐢, we can see that we are missing a few lengths. We’re missing the length 𝐴𝑀 and the length 𝐡𝐢.

Let’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 𝐢𝐷 is 10 centimeters and also that our side 𝐡𝐢 must be 11 centimeters. So now, if we look at our length 𝐴𝑀, which is part of the diagonal 𝐴𝐢, 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 𝐷𝑀 is equal to our length 𝑀𝐡. And importantly for us here, we now know that the length 𝐢𝑀 is equal to the length 𝐴𝑀, giving us that our final missing length is 8.6 centimeters.

So to find our perimeter of triangle 𝐴𝐡𝐢, 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 𝐴𝐡𝐢.

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