Question

Geometry! Please help!

Answer 1

The height of the trapezoid is 3cm. Let me know if you would like an explanation!

Answer 2

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

$Length\times breadth\\\\=5\times 13\\\\=65\ sq.\ cm$

Dimensions of trapezoid as follows:

Length of two parallel sides are 'a' = 11 cm

and 'b' = 13 cm

So, Area of trapezoid would be

$\dfrac{1}{2}\times (a+b)\times h\\\\=\dfrac{1}{2}\times (11+13)\times h\\\\=\dfrac{1}{2}\times 24\times h\\\\=12\times h$

Since the total area of composite shape = 101 sq. cm

Area of composite shape = Area of trapezoid + Area of rectangle

$101=65+12h\\\\101-65=12h\\\\36=12h\\\\\dfrac{36}{12}=h\\\\h=3\ cm$

Hence, the height of the trapezoid is 3 cm.