The shaded figure below is composed of a trapezoid and a semicircle on a coordinate plane.
which of the following expressions represents the area of the shaded figure?
(figure and choice is in pic.)

The area of shaded region is:

                 2(12+π) square units.

We have the trapezium as:

Length of one base i.e. CD is:8 units.

Length pf other base i.e. AB is: 4 units.

Also height of trapezium is: 4 units.

Hence, Area of trapezium is: 1/2×4×(8+4)

                                              = 24 square units.

Similarly area of semicircle is: πr²/2

where r is the radius of the semicircle.

Clearly we have the diameter of semicircle as: AB=4 units.

Hence, Radius of semicircle is: 4/2=2 units.

Hence, Area of semicircle is: 2π square units.

Hence, area of shaded region is:

Area of semicircle+Area of Trapezium.

               =2π+24

                    =2 (12+π) square units.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.