1: Write a formula in factored form for the are of the adjacent shaded region. http://dcs.unl.edu/ishs_course_image...oject3g004.gif

2: Write a Formula in factored form for the are of the adjacent shaded region. http://dcs.unl.edu/ishs_course_image...oject3g005.gif

2. Originally Posted by omgitzbella
1: Write a formula in factored form for the are of the adjacent shaded region. http://dcs.unl.edu/ishs_course_image...oject3g004.gif

2: Write a Formula in factored form for the are of the adjacent shaded region. http://dcs.unl.edu/ishs_course_image...oject3g005.gif
For 1, the area of each of the hemispheres on the side is $\frac{1}{2}\pi r^2$. Therefore, the area of both of them combined is $\pi r^2$.
To find the area of the shaded regions, subtract $\pi r^2$ from the area of the rectangle, which is $8r \times 2r = 16r^2$.
Shaded region = $16r^2 - \pi r^2 = r^2(16-\pi)$.

For 2, subtract the area of the smaller square from the area of the bigger.
Shaded region = $(6a)^2 - (3b)^2 = 36a^2 - 9b^2 = 9(4a^2 - b^2)$.