AREA

Geometry Level 2

An equilateral triangle that has an area of 9 3 9\sqrt { 3 } is inscribed in a circle. What is the area of the circle?

6 π 6\pi 12 π 12\pi 9 π 9\pi 9 3 π 9\sqrt { 3 } \pi

Shreya R by Shreya R , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

4 solutions

Angelito Matibag
May 6, 2014

using the formula of area of n-sides polygon inscribed in a circle

Atriangle=1/2(nr^2sin(360/n)

9√3=1/2(3r^2sin(360/3))

r^2=12

Acircle=πr^2

Acircle=π(12)=12π

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I have solved the solution, the system gives me error.

ma pm - 1 year, 11 months ago

Area of equilateral triangle= ((sqrt3)/4) * a^2 Height= ((sqrt3)/2) *a (a=side length). median(height of equilateral triangle) of triangle divides each into 2:1 ratio. ANd 2/3 of height of triangle is the radius of circle. AREA of circle= pi * r ^ 2 (r=radius) So final ans is 12pi .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I THOUGHT THAT THE CIRCLE INSIDE THE triangle SO MY ANSWE WAS 9 π I DID NOT KNOW THAT inscribed MEEN OUTSIDE

Eng-Mostafa Zinedine - 7 years ago
Chicku Bobde
Jul 30, 2018

Area of circle will be greater than area of triangle therefore 12 pi only with logic

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ritam Baidya
Dec 4, 2014

BY using formula for an equilateral triangle i.e. (root3)/4 x (side)*2=9root3 thus side is 6cm. now from the circumcentre dropping 3 equals heights(A) inside the 3 small parts fot the eq.triangle.....3 x (1/2 x A X 6)=9root3 on solving we get A=root3..thus since it is a part of a median in the ratio 2:1 thus we get the Radius of the CIRCLE = 2root3....thus area of the circle is 12pi

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...