I have a 30-60-90 triangle and i need to find the area in simple radical form. It has a hyp of 2radical(6) and short leg is radical(6) and the long leg is radical(18). Can anyone help me...
2007-12-03 11:27:36 · 10 answers · asked by lusius188 1 in Science & Mathematics ➔ Mathematics
Area = 1/2 * base * height.
Take the base and height to be the two sides forming the right angle and just plug the numbers in:
Area = 1/2 * radical(6) * radical(18)
You can simplify if you want:
= (1/2)radical(108)
=(1/2)radical(36*3)
=(1/2)radical((6^2)*3)
= 3radical(3)
2007-12-03 11:29:50 · answer #1 · answered by _asv_ 3 · 0⤊ 0⤋
well the area of a triangle is (1/2) (base*height) the base is the shortest side which is the side with radical (6) and the height is the longest leg which is the radical (18) so just multiply both of them and you get radical(108) and then you have to simplify the radical. you have to find a multiple of 108 that is a perfect square you could 36 b/c 36*3=108 and to write in radical form would be radical(36)*radical(3). but since 36 is a perfect square you can simplify it more. the square root of 36 is 6 and now ur answer is 6radical(3) but remember the area of a triangle is only half of that and so it is 6radical(3) divided by two. so you now have 6radical(3)/2. but you can divide the 6 and 2 and ur final answere is 3radical(3). and that is it. just remember the side opposite the 30 degree angle is always the shortest side and hypotenuse is always twice the lenght of the shortest side and the longest if you multiply the shotrtest side by radical(3) you can get its length hope this helps
2007-12-03 11:40:12 · answer #2 · answered by ooe4eva 5 · 0⤊ 0⤋
This is a right triangle because in a right triangle a^2 + b^2 = c^2 (Pythagorean Theorem) 9^2 + 12^2 = 225 square root of 225 is 15. So the triangle is right, and the base is 9, so the hypotenuse is 15, and h = 12. A = 1/2 bh A = 1/2 (12)(9) = 54 square inches I think that's correct. Hope it helps! =D
2016-05-28 01:37:10 · answer #3 · answered by ? 3 · 0⤊ 0⤋
If your angles are 30/60/90 degrees, you know you have a right triangle. The formula for the area is base * height * 1/2. You can figure it out by yourself, correct?
2007-12-03 11:30:53 · answer #4 · answered by tkquestion 7 · 0⤊ 0⤋
With a right triangle, area is easy: it is 1/2 base * height.
So the area is 1/2 * sqrt(6) * sqrt(18) = 1/2 sqrt(108) = 1/2 (6) sqrt(3)
Area = 3sqrt(3)
Best of luck!
2007-12-03 11:30:53 · answer #5 · answered by disposable_hero_too 6 · 0⤊ 0⤋
One half base times height. Just like the area of any triangle.
2007-12-03 11:30:21 · answer #6 · answered by Chris S 2 · 0⤊ 0⤋
From Geometry I remember it's 1 half times base times height
2007-12-03 11:30:08 · answer #7 · answered by Anonymous · 0⤊ 0⤋
multiply the two shortest sides and divide by 2
2007-12-03 11:30:37 · answer #8 · answered by I'm an Atheist 3 · 0⤊ 0⤋
write as another detail what the base and height are...
2007-12-03 11:30:36 · answer #9 · answered by kevinj8us 2 · 0⤊ 0⤋
a=b*h/2
a-area
b-base
h-height
2007-12-03 11:31:27 · answer #10 · answered by Drake Perrior-Small 2 · 0⤊ 0⤋