Find the area of an equilateral triangle with radius 8√3 m. Leave your answer in simplest radical form.
A. 5625√ 3 m2
B. 1875/2 √ 3 m2
C. 25/4 √ 3 m2
D. 5625/2 √ 3 m2
2007-05-16 05:09:19 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
An equilateral triangle has no radius!
That's reserved for circles.
So let's suppose you mean "side".
I'll let you convince yourself(draw a picture)
that the area of an equilateral triangle with
side s is s²√3/4.
So in your case, the area is 192√3/4 = 48√3.
None of your choices works.
2007-05-16 05:19:23 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
None of those choices work.
There are two things you can possibly mean by radius.
1) an equilateral triangle inscribed in a circle of radius r.
Search Yahoo answers, you see that that was previously answered.
A = 3*sqrt(3) / 4 * r^2 = 288 * sqrt(3)
2) OR you mean the side of the triangle is 8*sqrt(3)
A = 1/2 * [8*sqrt(3)]^2 * sin60
= 48 * s qrt(3)
The question is what do you mean by radius?
2007-05-16 05:25:04 · answer #2 · answered by Dr D 7 · 0⤊ 0⤋
Triangles do not have a radius, circles do. Is this a trick question?
If you mean that from the center of the triangle to any corner of the triangle is = 8(1.73)m = 13.86m, then the area is 499.1m^2.
2007-05-16 05:38:04 · answer #3 · answered by stone w 2 · 0⤊ 0⤋
The radius is 2/3 of the height, so height must be 12â3. Height is â3 times half the base, so half the base is 12. Area is half base times height, so 12 ( 12â3) = 144â3.
2007-05-16 05:18:27 · answer #4 · answered by Philo 7 · 0⤊ 1⤋
Triangles don't have a radius. Circles do. Maybe you mean height instead of radius?
2007-05-16 05:14:00 · answer #5 · answered by RedSox26 2 · 0⤊ 0⤋