Answer:
160 m²
384 m²
Step-by-step explanation:
The area of a trapezium is given by :
A = 1/2(a + b)h
h = height ; a and b = lengths
From the diagram :
A = 1/2(12 + 20)10
A = 1/2(32)10
A = 16 * 10
A = 160 m²
2.)
Area of parallelogram = base * height
Base = 24 ; h = 16
A = 24 * 16
A = 384 m²
Use the general form:-
(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the centre and r = radius
Here the radius = 1/2 * 6 = 3 so r^2 = 9 and we have the equation:-
(x + 4)^2 + (y - 2)^2 = 9 (answer)
we have

The solution is the shaded area above the dotted line
we know that
If a point is a solution of the inequality, then the coordinates of the point must satisfy the inequality
We will verify all cases to determine the solution of the problem
<u>Case A)</u> Point 

Substitute the value of x and y in the inequality and verify

-------> is not true
therefore
the point
is not a solution of the inequality
<u>Case B)</u> Point 

Substitute the value of x and y in the inequality and verify

-------> is true
therefore
the point
is a solution of the inequality
<u>Case C)</u> Point 

Substitute the value of x and y in the inequality and verify

-------> is not true
therefore
the point
is not a solution of the inequality
<u>Case D)</u> Point 

Substitute the value of x and y in the inequality and verify

-------> is not true
therefore
the point
is not a solution of the inequality
therefore
<u>the answer is the Point B</u>

To better understand the problem see the attached figure