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

Given that π΄π΅πΆπ· is a rectangle, find the perimeters of β³πΆπ·πΈ and π΄πΉπ΅πΆπΈπ·.

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### Video Transcript

Given that π΄π΅πΆπ· is a rectangle, find the perimeters of triangle πΆπ·πΈ and π΄πΉπ΅πΆπΈπ·.

Letβs firstly consider our properties of a rectangle. A rectangle has two pairs of equal length and parallel sides. Therefore, π΄π· is equal to π΅πΆ and π΄π΅ is equal to π·πΆ. This means that the length of π΄π· is 22 centimetres, and the length of π·πΆ is 11 centimetres. The triangles at either end, π΄π΅πΉ and πΆπ·πΈ, are isosceles. This means that two of the sides are equal in length. Length π·πΈ is equal to πΆπΈ, and length π΄πΉ is equal to length π΅πΉ. All four of these sides are equal to eight centimetres.

The perimeter of any shape is the distance around the outside. Letβs firstly consider triangle πΆπ·πΈ. 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 πΆπ·πΈ is 27 centimetres.

Now, letβs consider the six-sided shape or hexagon π΄πΉπ΅πΆπΈπ·. 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 π΄πΉπ΅πΆπΈπ· is 76 centimetres.