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

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

answer: 3.26019516

step-by-step explanation: