Question

The above 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 $y=9-x^2$. Calculate the area of rectangle $ABCD$ if point B has coordinates $(-1.50,6.75)$.

• A. $12.50$
• B. $17.50$
• C. $22.75$
• D. $26.50$
• E. $30.75$

Answer 1

The correct option is C $22.75$

Given, $A$ and $D$ are on parabola $y=2x^2-8$

And point $B$ and $C$ are on parabola $y=9-x^2$

And coordinates point $B$ is $(-1.50,6.75)$

Then coordinates point $C$ is $(1.50,6.75)$

The $ABCD$ is a rectangle

Then $x$ coordinates point $A$ is $(-1.50)$

So $y$ coordinates $=$ $y=2x^2-8=2(-1.50{)}^2-8=4.5-8=-3.5$

Then coordinates point $A$ is ($-1.50,-3.50)$

And coordinates point $D$ is $(1.50,-3.50)$

Then length of line $AD=1.50+1.50=3$

And length of line $AB=6.75+3.50=10.25$

Then area of rectangle $=$ $10.25\times 3=30.75$.