Me! what is the area of trapezoid defg with coordinates d(4, 3), e(4, 0), f(2, 1), and g (2, 3)?

the area of the trapezoid is 5 units²

step-by-step explanation:

* lets check the sides of the trapezoid

- the trapezoid has two parallel bases

- its height is perpendicular to the parallel bases

- the vertical segment has same x-coordinates and its length is the

  difference between the y-coordinates

- ex: the segment whose endpoints are (3 , 5) and (3 , -2) is vertical and

  its length = 5 - -2 = 5 + 2 = 7

- the horizontal segment has the same y-coordinates and its length

  is the difference between the x-coordinates

- ex: the segment whose endpoints are (2 , 5) and (6 , 5) is horizontal

  and its length = 6 - 2 = 4

* lets solve the problem

∵ defg is a trapezoid

∵ d (4 , 3) , e (4 , 0) , f (2 , 1) , g (2 , 3)

∵ point d and e have same x-coordinates

∴ de is a vertical segment

∴ the length of de = 3 - 0 = 3 units

∵ point f and g have same x-coordinates

∴ fg is a vertical segment

∴ the length of fg = 3 - 1 = 2 units

∵ de and fg are vertical segments

∴ de // fg

- the bases of the trapezoid are ef and eg

∵ d and g have the same y-coordinates

∴ dg is a horizontal segment

∴ the length of dg = 4 - 2 = 2 units

∵ the horizontal distance is ⊥ to the vertical distance

∴ dg ⊥ de and dg ⊥ fg

∴ dg is the height of the trapezoid

- the area of trapezoid = 1/2 (base1 + base2) × (height)

∵ de and fg are its bases

∵ dg it height

∵ de = 3 , fg = 2 , dg = 2

∴ its area = 1/2 (3 + 2) × 2 = 5 units²

step-by-step explanation: yes

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