Area - circles and equilateral triangle.

**ejaykasai** · October 14th 2010, 12:20 AM

1. Find the area of the shaded region. this triangle is equilateral all sides are 2.

Thanks for helping!

**HallsofIvy** · October 14th 2010, 03:38 AM

You have an equilateral triangle with sides of length 2. If you drop a perpendicular from one vertex of the triangle to the opposite side, you divide the triangle into two right triangles with hypotenuse 2 and one leg 1. You can use the Pythagorean theorem to determine that $x^2+ 1^2= 2^2$ , $x^2= 4- 1= 3$ , $x= \sqrt{3}$ : the other leg has length $\sqrt{3}$ , the altitude of the triangle. From that you can calculate the area of the triangle.

Each of the three circles has radius 1 and so area $\pi$ . Each angle of the triangle is 60 degrees which is 60/360= 1/6 of the complete circle. That is, each of the sectors of a circle has area $\frac{\pi}{6}$ .

The shaded area is the area of triangle minus the three sector areas.

Thread: Area - circles and equilateral triangle.

LinkBack

Thread Tools

Display

Area - circles and equilateral triangle.

Similar Math Help Forum Discussions

6 Equal circles in an equilateral triangle

Circle Geometry: Circles in A Equilateral Triangle

area of an equilateral triangle

Find the area of an equilateral triangle with side length 14.

Series of Circles inscribed in an equilateral Triangle

Search Tags