SOLUTION: Find the area of an equilateral triangle in which each side has a length of 2cm.

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Question 221444: Find the area of an equilateral triangle in which each side has a length of 2cm.
Answer by drj(1380) About Me  (Show Source):
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Find the area of an equilateral triangle in which each side has a length of 2cm.

Step 1. Area of equilateral triangle is A=bh%2F2 where b is the base and h is the height. Draw a perpendicular line from one angle to the midpoint of the opposite side. Doing this forms a right triangle and bisected in half the opposite side.

Step 2. The base is 1/2 the side of the equilateral triangle or 2cm/2=1 cm.

Step 3. The height can be calculated using the Pythagorean Theorem which states that the sum of the squares of the legs of a right triangle (h and b) is equal to the hypotenuse squared or side s=2 cm.

Then, s%5E2=h%5E2%2Bb%5E2

2%5E2=h%5E2%2B1%5E2

4=h%5E2%2B1

h%5E2=3

h=sqrt%283%29

Step 4. ANSWER: Area A=bh%2F2=1%2Asqrt%283%29%2F2=sqrt%283%29%2F2 square centimeters.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J