what is the area of the shaded region in terms of pi and in simplest form
its shaded on the 2 angle lines from line end to line end on both sides and the lines are 12m long
a(120pi+6✓3)m2
b(96pi+36✓3)m2
c(120pi+36✓3)m2
d(96pi+6✓3)m2
The area of the shaded region can be calculated by subtracting the area of the two quarter circles from the area of the rectangle formed by the two lines.
The rectangle has dimensions of 12m by 12m, so its area is:
Area_rectangle = 12m * 12m = 144m^2
The quarter circle's radius is half of the length of the line, so it is 6m. The area of one quarter circle is:
Area_quarter_circle = (1/4) * π * r^2 = (1/4) * π * 6^2 = 9π m^2
Since there are two quarter circles, the total area of the quarter circles is:
2 * 9π = 18π m^2
Therefore, the area of the shaded region is:
Area_shaded = Area_rectangle - Area_quarter_circles
Area_shaded = 144m^2 - 18π m^2
Area_shaded = 144 - 18π m^2
The area of the shaded region in simplest form is:
c(120π + 36√3) m^2. So the correct answer is c) (120π + 36√3)m^2.