Question

Geometry! Please help!

This composite shape has an area of 101 cm².

What is the height of the trapezoid?

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.

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* breadth\\\\=5* 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

`(1)/(2)* (a+b)* h\\\\=(1)/(2)* (11+13)* h\\\\=(1)/(2)* 24* h\\\\=12* 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\\\\(36)/(12)=h\\\\h=3\ cm`

Hence, the height of the trapezoid is 3 cm.