When equilateral triangle OAB with sides of length 4 lies on parabola y=ax squared(a>0) as shown below, solve the following problems.

Question

2) Find the value of a
substituting the coordinates of point A into y=ax squared
3) Find the area S of equilateral triangle OAB

Answer 1

2) Since point A lies on the parabola, we have:
y = ax^2
Substitute the coordinates of point A (2, 4) into the equation:
4 = a(2)^2
4 = 4a
a = 1

Therefore, the value of a is 1.

3) To find the area of equilateral triangle OAB, we first need to find the height of the triangle. The height of an equilateral triangle can be calculated using the formula:
height = (sqrt(3)/2) * side length

For the given triangle OAB with side length 4:
height = (sqrt(3)/2) * 4
height = 2sqrt(3)

Now we can calculate the area of the equilateral triangle using the formula:
Area = (1/2) * base * height
Area = (1/2) * 4 * 2sqrt(3)
Area = 4sqrt(3)

Therefore, the area of equilateral triangle OAB is 4sqrt(3) square units.