Question 1209964
<pre>
The other tutor (artificial intelligence) has the wrong answer.  It probably
can't read the numbers on the drawing on the site like a human can. The drawing
on the site is off scale and on the site it looks as though if you extended AF,
it would pass through E, but this is not the case.

{{{drawing(170,580,-1,5,-1,24,

line(0,0,4,0),
line(0,3,4,0),
line(0,23,4,20),
line(0,0,0,23),
line(0,23,4.86,22.3),
line(4,0,4,20), 

arc(0,23,10,-10,-37,-7),

locate(1.3,22.98,35^o),


locate(0,0,B), locate(4,0,A), locate(4.2,20.3,F), locate(4.74,23.2,E),
locate(0,23.8,D) , locate(-.44,1.7,3), locate(1.7,0,4), locate(4.2,11,20),
locate(-.44,3.3,C)
)}}} 

Area of parallelogram = (AB)(AF) = (4)(20) = 80 cm<sup>2</sup>

Area of right triangle ABC = {{{expr(1/2)*AB*BC=expr(1/2)*4*3}}} = 6 cm<sup>2</sup>

To find the area of sector DEF, we must first find the radius.

The radius DF is equal to {{{AC=sqrt(AB^2+BC^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5}}}

The area of the sector is {{{35/360}}}ths of the area of a circle with the same
radius.

So the area of sector is {{{expr(35^o/360^o)*pi*5^2=expr(175/72)pi}}}cm<sup>2</sup>

So adding the parallelogram, right triangle and sector:

{{{80 + 6 + expr(175/72)pi = 86+expr(175/72)pi}}} or about 93.63581548 cm<sup>2</sup>  

Edwin</pre>