If a=6cm, find the area of the equilateral triangle. Round the answer to one decimal place.
draw in the height, and you will have a 30-60-90 right-angled triangle
height^2 + 3^2 = 6^2
height^2= 36-9 = 27
height = √27
area = (1/2)base x height = (1/2)(6)√27 = 9√3
= 15.6
To find the area of an equilateral triangle, you need to know the length of one side of the triangle (often represented by the variable "a"). In this case, you are given that a = 6 cm.
The formula to calculate the area of an equilateral triangle is:
Area = (√3/4) * a^2,
Where "a" is the length of one side of the triangle.
Plugging in the given value, the formula becomes:
Area = (√3/4) * (6cm)^2.
Now, let's calculate the value:
Area = (√3/4) * 36 cm^2.
Next, simplify the expression:
Area = (1.732/4) * 36 cm^2.
Now, multiply the numerator and denominator by 9 to get a whole number numerator:
Area = 7.794 cm^2.
Finally, round the answer to one decimal place:
Area ≈ 7.8 cm^2.
So, the area of the equilateral triangle is approximately 7.8 cm^2.