I need help solving these math problems, I have no idea how to do them:
the circle one I need the are aof the shaded figure
the p-gram one, i need the area
the pentagon, I need the apothem, area, and side length
The area of the shaded regions in the circle.
The sides of the triangle with hypoteneuse 6 inches are the same, They are the radius of the circle:
The subtended angle is 90 degrees.
Area of circular segment:
That's one of them. Multiply by 2.
For the rhombus, find the area of one of the right triangles and multiply by 4.
Ok so basically we have that
where a is apothem and p is permieter
Now since we know that the exterior angle of a n-gon is we know due to the linear pair postulate that the interior angle of an n-gon is
so for a pentagon(5-gon)
the interior angle would be
So now we know that the angle at a vertex is 108 we know that the apothem bisects it making
the angle that the apothem cuts off 44...so now we have a right triangle with angles ,90,44,46
So we need to calculate the apothem or in this case we are given it but we need to find sidelenght
so we use trig
and since that gives us half of our side we see that the sidelenghts are
now we go to our formula
Now since where n is the sidelength we see that
so now we see