Question Video: Finding the Perimeter of a Composite Figure given the Lengths of Some of Its Sides Mathematics

Given that 𝐵𝐶𝐷𝐸 is a square, find the perimeter of 𝐴𝐶𝐷𝐸.

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Video Transcript

Given that 𝐵𝐶𝐷𝐸 is a square, find the perimeter of 𝐴𝐶𝐷𝐸.

The perimeter of any shape is the distance around the outside. As 𝐵𝐶𝐷𝐸 is a square, all four sides of the shape will be equal in length. As 𝐶𝐷 is equal to eight centimeters, then 𝐷𝐸 and 𝐵𝐶 will also be equal to eight centimeters. The length 𝐵𝐸 would also be equal to eight centimeters. However, this is not on the outside of the shape.

The perimeter of shape 𝐴𝐶𝐷𝐸 will be the sum of the five lengths 𝐴𝐵, 𝐵𝐶, 𝐶𝐷, 𝐷𝐸, and 𝐸𝐴. These are equal to 15 centimeters, eight centimeters, eight centimeters, eight centimeters, and 17 centimeters, respectively. Eight plus eight plus eight is equal to 24. We need to add 15, 24, and 17. We can add these in any order. 15 plus 24 is equal to 39. Adding 17 to this gives us 56.

The perimeter of 𝐴𝐶𝐷𝐸 is 56 centimeters.