and what is that ?
The plane area shown in the figure consists of an isosceles trapezoid(non-parallel sides equal) and a segment of a circle. If the non-parallel sides are tangent to the segment at points A and B, find the area of the composite figure.
Where should I start in this problem?
assume your is for as shown in my attached figure.
I have worked out a pretty complicated, perhaps stupid, method...
produce all the lines and points as shown in figure, such that
AO = WO = BO = radius of a circle. O is centre of the circle.
AOZ, BOX and WOY are all straight lines.
AC//WY//BD and they are all perpendicular to both AB and EF
since AE and BF are tangents, = = hence = = , and
so we have a equilateral triangle ABO, with AO = BO = AB = 3
you can prove that WOY is bisector of angles AOB and XOZ, therefore
Given that WOY = 5 and assumed that WO = 3, hence OY = 2
In triangle YOZ,
therefore AZ =
In triangle CAZ,
In triangle EAC,
The area of sector AWBO
and the area of triangle ABO
Therefore the area of region AWB (green in figure)
= area of sector AWBO - area of triangle ABO
area of trapezium AEFB
.....in the end you will get this area = 50.4138
So the area of overall figure = 50.4138 + 0.8153 = 51.2291 ( ??)