Question

The shaded figure below is composed of a trapezoid and a semicircle on a coordinate plane.

Answer 1

Answer:

The area of shaded region is:

                 2(12+π) square units.

Step-by-step explanation:

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.

Answer 2

First, calculate for the area of the trapezoid. 
                           A = 0.5(b1 + b2)h
From the figure, b1 and b2 are 4 and 8. The height is 4. Substituting,
                          A = 0.5(4 + 8)(4)
                           A = 24

For the semicircle, the area would be,
                           A = 0.5πr²
Substituting,
                            A = 0.5(π)(2²) = 2π

Thus, the answer to this item would be 2(12 + π), the first choice.