Answer: The height of the trapezoid is 3 cm.
Step-by-step explanation:
Since we have given that
There is a trapezoid over the rectangle.
Dimensions of rectangle is as follows:
Length = 5 cm
Breadth = 13 cm
So, Area of rectangle would be
![Length\times breadth\\\\=5\times 13\\\\=65\ sq.\ cm](https://tex.z-dn.net/?f=Length%5Ctimes%20breadth%5C%5C%5C%5C%3D5%5Ctimes%2013%5C%5C%5C%5C%3D65%5C%20sq.%5C%20cm)
Dimensions of trapezoid as follows:
Length of two parallel sides are 'a' = 11 cm
and 'b' = 13 cm
So, Area of trapezoid would be
![\dfrac{1}{2}\times (a+b)\times h\\\\=\dfrac{1}{2}\times (11+13)\times h\\\\=\dfrac{1}{2}\times 24\times h\\\\=12\times h](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%28a%2Bb%29%5Ctimes%20h%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%2811%2B13%29%5Ctimes%20h%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2024%5Ctimes%20h%5C%5C%5C%5C%3D12%5Ctimes%20h)
Since the total area of composite shape = 101 sq. cm
Area of composite shape = Area of trapezoid + Area of rectangle
![101=65+12h\\\\101-65=12h\\\\36=12h\\\\\dfrac{36}{12}=h\\\\h=3\ cm](https://tex.z-dn.net/?f=101%3D65%2B12h%5C%5C%5C%5C101-65%3D12h%5C%5C%5C%5C36%3D12h%5C%5C%5C%5C%5Cdfrac%7B36%7D%7B12%7D%3Dh%5C%5C%5C%5Ch%3D3%5C%20cm)
Hence, the height of the trapezoid is 3 cm.