Figure shows rectangle ABCD. Points A and D are on the parabola `y = 2x^(2)-8`, and points B and C are on the parabola `y = 9-x^(2)`. If point B has coordinates `(-1.50, 6.75)`, what is the area of rectangle ABCD ?

Options

A. `12.50`
B. `17.50`
C. `22.75`
D. `30.75`

Answer

D

Explanation

To find the area of the rectangle, you need the base and height. Both parabolas are symmetric with respect to the y - axis, so if the x - coordinate of point B is - 1.50, the length of segment BC, which is the base of the rectangle, is twice 1.50, or 3. To find the height of the rectangle, use the y - coordinate of point B and find the y - coordinate of point A. That's the value of y when you plug `x = -1.50` into the equation `y=2x^(2)-8` :
`y=2(-1.50)^(2)-8=-3.5`
So the height of the rectangle is `6.75 - (-3.5)=6.7+3.5 = 10.25`, and the area of the rectangle is `3xx10.25=30.75`.