Question Video: Finding the Perimeters of a Composite Figure and One of Its Parts Mathematics

Video Transcript

Given that 𝐴𝐵𝐶𝐷 is a rectangle, find the perimeters of triangle 𝐶𝐷𝐸 and 𝐴𝐹𝐵𝐶𝐸𝐷.

Let’s firstly consider our properties of a rectangle. A rectangle has two pairs of equal length and parallel sides. Therefore, 𝐴𝐷 is equal to 𝐵𝐶 and 𝐴𝐵 is equal to 𝐷𝐶. This means that the length of 𝐴𝐷 is 22 centimetres, and the length of 𝐷𝐶 is 11 centimetres. The triangles at either end, 𝐴𝐵𝐹 and 𝐶𝐷𝐸, are isosceles. This means that two of the sides are equal in length. Length 𝐷𝐸 is equal to 𝐶𝐸, and length 𝐴𝐹 is equal to length 𝐵𝐹. All four of these sides are equal to eight centimetres.

The perimeter of any shape is the distance around the outside. Let’s firstly consider triangle 𝐶𝐷𝐸. This triangle has sides of length eight centimetres, eight centimetres, and 11 centimetres. Adding eight, eight, and 11 gives us 27. This means that the perimeter of triangle 𝐶𝐷𝐸 is 27 centimetres.

Now, let’s consider the six-sided shape or hexagon 𝐴𝐹𝐵𝐶𝐸𝐷. This shape has four sides of length eight centimetres and two sides of length 22 centimetres. Four multiplied by eight is equal to 32. Two multiplied by 22 is equal to 44. Therefore, the perimeter is equal to 32 plus 44. This is equal to 76. Therefore, the perimeter of the hexagon 𝐴𝐹𝐵𝐶𝐸𝐷 is 76 centimetres.