Question

Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale. 70 points answer in FULL detail PLEASE!!!!

Answer 1

Area of trapezoid = Area of middle rectangle + Area of the right triangle + Area of left triangle
Area of rectangle= 5cm*9cm=45cm^2
Area of right triangle= 0.5* 9cm *2cm=9cm^2
For the left triangle, its an isosceles triangle as the base angles are equal,
so area of left triangle= 9*9*0.5=40.5cm^2
Area of trapezoid= 40.5+45+9= 94.5cm^2

Answer 2

Explanation:

Consider ABCD be a trapezoid, then from ΔAED, we have

`(AE)/(DE)=tan45^(\circ)`

`(9)/(DE)=1`

`DE=9cm`

Then, area ΔAED is given as:

`A=(1)/(2){*}9{*}9`

`A=(81)/(2)cm^2`

Also, area ΔBCF is given as:

`A=(1)/(2){*}2{*}9`

`A=9cm^2`

And, area rectangle ABFE is given as:

`A=5{*}9`

`A=45cm^2`

Now,

Area of trapezoid ABCD =area ΔAED+area ΔBCF+area rectangle ABFE

=
`(81)/(2)+9+45`

=
`94.5cm^2`

Thus, the area of trapezoid ABCD is
`94.5cm^2`.