Thread: Area enclosed by chord and another similar problem

http://readyforgmat.com/math/documen...s-version2.pdf

Both the problems on page 15, especially #2.
Thanks.

In the first question, you need to note that the two triangles are similar. So the length of the sides in the second triangle are the same constant multiple of the length of the sides in the first triangle.

In the second question, you need to create a triangle using the chord and two radii. Evaluate the area of the sector and subtract the area of the triangle.

In the second question, you need to create a triangle using the chord and two radii. Evaluate the area of the sector and subtract the area of the triangle.

I understand how to create the triangle (I tried isosceles with side length 6). I believe the area of the triangle is 9 root 3.
The circle is of area 36pi, hence each quadrant of the circle should be of area 9pi

I don't know how to get the area of the blackened sector, though.

The sector is actually of the circle, so its area is actually .

So surely the blackened area is ...

Originally Posted by skyd171

I understand how to create the triangle (I tried isosceles with side length 6). I believe the area of the triangle is 9 root 3.
The circle is of area 36pi, hence each quadrant of the circle should be of area 9pi

The is equilateral. So that central angle is .
Thus the area of the whole sector is .
To find the shaded area, subtract the area of the triangle from the area of the sector.