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

Answer:

     

Step-by-step explanation:

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

$\frac{AE}{DE}=tan45^{\circ}$

$\frac{9}{DE}=1$

$DE=9cm$

Then, area ΔAED is given as:

$A=\frac{1}{2}{\times}9{\times}9$

$A=\frac{81}{2}cm^2$

Also, area ΔBCF is given as:

$A=\frac{1}{2}{\times}2{\times}9$

$A=9cm^2$

And, area rectangle ABFE is given as:

$A=5{\times}9$

$A=45cm^2$

Now,

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

=$\frac{81}{2}+9+45$

=$94.5cm^2$

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

Answer 2

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