Answer:
This is a long answer. I got 82.5
Step-by-step explanation:
Area of isoceles triangle is
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 know side FH=11
- We know Angle D equal 56
- We are trying to find side DF
- We know angle H equal 90
We can use law of sines to find side DF
Plug in the numbers
sin of 90 =1 so
Side df is about 13.3 inches.
Since we know our slanted side is 13.3 we can set up our pythagorean theorem equation,
is approximately 7.5 so dh=7.5 approximately.
Now using base times height times 1/2 multiply them out