05.05 hc) figure abcd has vertices a(−2, 3), b(4, 3), c(4, −2), and d(−2, 0). what is the area of figure abcd?

The area of ABCD is 24 units²

Step-by-step explanation:

* Lets explain how to solve the problem

- All the point in a vertical line have the same x-coordinates

- The length of the vertical line is y2 - y1

- All the point in a horizontal line have the same y-coordinates

- The length of the horizontal line is x2 - x1

- The horizontal and the vertical lines are perpendicular to each other

- The trapezoid has two parallel bases not equal in length and the other

 two sides are nonparallel sides

- The area of the trapezoid = 1/2 (sum of the two // bases) × height

* Lets solve the problem

∵ ABCD is a quadrilateral

∵ A = (-2 , 3) , B = (4 , 3) , C = (4 , -2) , D = (-2 , 0)

∵ Side AD has same x-coordinates in A and D (-2)

∴ AD is vertical side

∴ AD = 3 - 0 = 3

∵ Side BC has same x-coordinates in B and C (4)

∴ BC is vertical side

∴ BC = 3 - (-2) = 3 + 2 = 5

∵ AD and BC are vertical lines

∴ AD // BC

∵ Side AB has same y-coordinates in A and B (3)

∴ AB is horizontal side

∴ AB = 4 - (-2) = 4 + 2 = 6

∵ The horizontal and the vertical lines are perpendicular to each other

∴ AB is perpendicular on AD and BC

∵ The side CD is not vertical or horizontal

∴ ABCD has only two parallel sides AD and BC

∵ AD ≠ BC

∴ ABCD is a trapezoid

∵ The two parallel bases are AD and BC

∵ Its height is AB

∵ AD = 3 , BC = 5 , AB = 6

∴ Its area = 1/2 (3 + 5) × 6 = 1/2 (8) × 6 = 4 × 6 = 24 units²

* The area of ABCD is 24 units²

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

1/6

step-by-step explanation: