Answer:
This is a long answer. I got 82.5
Step-by-step explanation:
Area of isoceles triangle is
[tex] \frac{1}{2} (b)(h)[/tex]
where b is the base and h is height.
Let draw a altuide going through Point D that split side FE into 2 equal lines. Let call that point that is equidistant from FE, H.
Since it is a altitude,it forms a right angle. So angle H=90.
Angle H is equidistant from F and E so
FH=11
EH=11.
The height is still unknown.
We can use pythagorean theorem to find side h but we need to know the slanted side or side DF to use the theorem.
Using triangle DFH, we know that angle H is 90 and angle F is 34. So using triangle interior rule,Angle D equal 56.
We can use law of sines to find side DF
[tex] \frac{fh}{ \sin(d) } = \frac{df}{ \sin(h) } [/tex]
Plug in the numbers
[tex] \frac{11}{ \sin(56) } = \frac{df}{ \sin(90) } [/tex]
sin of 90 =1 so
[tex] \frac{11}{ \sin(56) } = df[/tex]
Side df is about 13.3 inches.
Since we know our slanted side is 13.3 we can set up our pythagorean theorem equation,
[tex](fh) {}^{2} + (dh) {}^{2} = df {}^{2} [/tex]
[tex](11) {}^{2} +( dh) {}^{2} = (13.3) {}^{2} [/tex]
[tex]121 + dh {}^{2} = 176.89[/tex]
[tex](dh) {}^{2} = 55.89[/tex]
[tex] \sqrt{55.89} = 7.5[/tex]
is approximately 7.5 so dh=7.5 approximately.
Now using base times height times 1/2 multiply them out
[tex] \frac{1}{2} (22)(7.5)[/tex]
[tex]82.5[/tex]