How do you find the area of a circle inscribed in a equilateral triangle?

The only thing you know is the length of a side is 14 cm. PLEASE HELP!

also, could you find the area of the part not included in the circle?

Draw the radius of the circle from the bottom middle of the triangle to the circle’s center. Then draw a line from the circle’s center to the left vertex of the triangle. As you can clearly see, you now have a 30-60-90 triangle with one leg equal to 7 cm.

From the 30-60-90 ratio that s√3:s:2s

s√3=7

s=7√3/(3)=radius

Area of circle=pi*r^2

Area=pi*49*3/9=49pi/3

This entry was posted on Sunday, January 17th, 2010 at 4:24 am and is filed under circle area. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “How do you find the area of a circle inscribed in a equilateral triangle?”

MechEng2030 on January 17th, 2010 at 9:46 am

Draw the radius of the circle from the bottom middle of the triangle to the circle’s center. Then draw a line from the circle’s center to the left vertex of the triangle. As you can clearly see, you now have a 30-60-90 triangle with one leg equal to 7 cm.

From the 30-60-90 ratio that s√3:s:2s

s√3=7

s=7√3/(3)=radius

Area of circle=pi*r^2

Area=pi*49*3/9=49pi/3
References :

Area List