The perimeter of a quadrilateral is the total length of its boundary. This is gotten by finding the sum total of the lengths of each side.
The perimeter of the outer square is 76 cm. This means that the outer length of each trapezium, given that they are all identical is:
![\Rightarrow(76)/(4)=19\operatorname{cm}]()
The perimeter of the inner square is 60 cm. This means that the inside length of each trapezium is:
![\Rightarrow(60)/(4)=15\operatorname{cm}]()
To calculate the area of a trapezium, we make use of the formula:
where a and b are the parallel sides and h is the height of the trapezium.
As it stands, we have calculated the length of the parallel sides of the trapezium and are left with the height to work out. This we can work by subtracting the outer length and inner length and dividing the result by 2 (to account for the 2 sides of the mirror). This will give us the thickness/height of the trapezium:
![\Rightarrow(19-15)/(2)=(4)/(2)=2\operatorname{cm}]()
Therefore, each trapezium is as shown below:
Hence, using the parameters:
we can calculate the area to be:
![\begin{gathered} A=(1)/(2)(19+15)*2 \\ A=19+15 \\ A=34\operatorname{cm}^2 \end{gathered}]()
The area of each trapezium is 34 cm².