PLEASE HELP ME PLEASE A triangle is inscribed in a square, as shown. Write a simplified function r in terms of x that represents the area of the shaded region.

This is the same as (1/2)x^2 because 1/2 = 0.5

We could rewrite that into

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Explanation:

The base of the white triangle (aka unshaded region) is x, while the height is also x

The area of the white triangle is

A = 0.5*base*height

A = 0.5*x*x

A = 0.5*x^2

The area of the entire square is x*x = x^2. Subtract off the area of the white triangle to get the area of the two blue shaded regions combined

shaded region = (square area) - (white triangle area)

shaded region = (x^2) - (0.5x^2)

shaded region = x^2 - 0.5x^2

shaded region = 1x^2 - 0.5x^2

shaded region = (1-0.5)x^2

shaded region = 0.5x^2

So the white triangle occupies half of the square, while the blue shaded region occupies the remaining 50% of the square.

Because 0.5 = 1/2, we can write this as (1/2)x^2, but I think using decimals in this case is easier.