SOLUTION: Suppose you have an equilateral triangle with a height of h feet. Then its area is A= square feet. Hint: Draw the right triangle and its height. The area of the triangle equ

Question 1103623: Suppose you have an equilateral triangle with a height of h feet. Then its area is
A= square feet.
Hint: Draw the right triangle and its height. The area of the triangle equals of base times height. You know the height. Use the Pythagorean Theorem to figure out the base. Use sqrt() to enter the square root of something.
Found 2 solutions by Boreal, addingup:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A=(1/2)bh
The side is s.
The altitude divides the equilateral triangle into 2 30-60-90 triangles, because the altitude is a bisector of one of the 60 degree angles.
The sine of 30 degrees is the opposite side (or half s) over the hypotenuse, or s.
The Pythagorean theorem has the hypotenuse squared (s^2)= opposite side squared (s/2)^2 plus the adjacent side, the altitude, which is (s/2) sqrt (3) or h.
Therefore h=(s/2) sqrt(3)
The area is (1/2)s*(s/2) sqrt (3) or (s^2/4)sqrt(3) ft^2.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
The area of a triangle is not base * height. It is:
A = 1/2(b*h)
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- All sides of an equilateral triangle are the same length. So we call it the side length as opposed to, for example, the base, side, hypotenuse in a right triangle.
.
- The interior angles of an equilateral triangle are each 60�.
.
- When drawing the height you are cutting the base in half (see pic below), so you end up with two identical right triangles with angles 30-60-90.
.
- Let's call the side lengths s. The ratio of a 30-60-90 is 1:sqrt(3):2 (all you need to know here is that this translates into the height of an equilateral is:
h = s/2*sqrt(3), then s = h/sqrt(3). With this information, calculate the area:
A = 1/2(s*h)

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