What is the area and perimeter of an equilateral triangle with height 2.?

Answer 1

Peremiter

6 inches

Area

2inches square

Answer 2

If the height is 2, then a 30°-60°-90° triangle formed by the height would have a short side of [2 / (√3)], or 2√3 / 3. The hypotenuse (which is one side of the equilateral triangle) is twice that, thus 4√3 / 3.

A = bh / 2
A = (4√3 / 3)(2) / 2
A = 4√3 / 3

P = 3(4√3 / 3)
P = 4√3

Answer 3

ok we have an equilateral triangle
let's name the height with ha and its sides with a, b and c,from here results that a=b=c and that ha=2=a√3/2 so a√3=4
a=4/√3=4√3/3
the area is A=a*√3/4=16√3/3¤1/4=4√3/3 (* means here 2 and ¤ means multiplication)
the perimeter is P=(4√3/3)¤3=12√3/3=4√3
so the final result is:A=4√3/3 and P=4√3

Answer 4

The ratio of the height to the base of an equilateral triangle is
sqrt3 : 2 which is the same as 1 : (2(sqrt3)/3).
Here we have height of 2 which implies that the base is
4(sqrt3)/3.
Therefore the area of this triangle is 0.5 *((4sqrt3)/3))*2
=4(sqrt3)/3.
The perimeter= 3*4(sqrt3)/3 =4sqrt3

Answer 5

h = 2

If we draw the height we get a 30 by 60 by 90 triangle

applying trigonometry we get the value 2/sqrt3 as the shorter side and 4/sqrt3 as the hypotenuse

the hypotenuse of the newly made triangle is the side of the equilateral triangle so the perimeter would be

p = 3 * (4/sqrt3)

p = 12/sqrt3

The area would be bh/2

a = ((4/sqrt3) * 2)/2

a = 4sqrt3

Tada!!!

Answer 6

You must use the ratios that exist in 30-60-90 degree triangles to figure this out. Each side has a length of 4sqrt3/ 3 which makes :

p = 4sqrt3

a = 4sqrt3 / 3

Answer 7

perimeter= 3 root 2
area= root 2

Answer 8

given the height = 2 then let the sides = x

from pythogras = x squared - 4 -(0.5 *x) = 0
solve = x = square root of 3
perimeter = 3*square root of 3(in normal units)

area = 0.5 * square root of 3 * 2 = square root of 3 (in square units)

Answer 9

Perimeter = 6.92820323
Area = 2.30938721

Answer 10

h = a * sqrt(3)/2
2 = a * sqrt(3)/2
4 = a * sqrt(3)
4/sqrt(3) = a
a = (4sqrt(3))/3
a = (4/3)sqrt(3)

P = 3a
P = 3((4/3)sqrt(3))
P = 4sqrt(3)

Area = a^2 * sqrt(3)/4
Area = (16/3) * sqrt(3)/4
Area = ((16/3)/4)sqrt(3)
Area = ((16/3)/(4/1))sqrt(3)
Area = ((16/3)*(1/4))sqrt(3)
Area = (16/12)sqrt(3)
Area = (4/3)sqrt(3)

Perimeter = 4sqrt(3) or about 6.928
Area = (4/3)sqrt(3) or about 2.309