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
[tex]Length\times breadth\\\\=5\times 13\\\\=65\ sq.\ cm[/tex]
Dimensions of trapezoid as follows:
Length of two parallel sides are 'a' = 11 cm
and 'b' = 13 cm
So, Area of trapezoid would be
[tex]\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[/tex]
Since the total area of composite shape = 101 sq. cm
Area of composite shape = Area of trapezoid + Area of rectangle
[tex]101=65+12h\\\\101-65=12h\\\\36=12h\\\\\dfrac{36}{12}=h\\\\h=3\ cm[/tex]
Hence, the height of the trapezoid is 3 cm.
