ISOSCELES TRIANGLE

First I'd recommend getting out a piece of paper and drawing the parabola and triangle.

The triangle right angled vertex is at (0,0). The two equal legs radiate out from this vertex along the mutually perpendicular lines y=x and y=-x.

Since the triangle is inscribed in a parabola y^2=4x the other two vertices are intersections of these lines with the parabola y^2=4x.

The other two triangle vertices are at (4,4) & (4,-4) Right? So the vertices of the triangle is at (0,0), (4,4) & (4,-4) & the base is coincident with the line vertical x=4.

The area of a triangle is 1/2 times the base and the height. The base is the difference in x between the right angle vertex and the base line (wy=4-0=4). The base is the difference between the y's on the base line (b=4-(-4)=8)

Now plug in b and h to find the triangle area.

Rap