Answer:
74.1 units²
Step-by-step explanation:
Area of the trapezoid shown = ½×(AD + BC)×BE
Use distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to find AD, BC, and BE.
✍️Distance between A(-9, 4) and D(9, 1):
[tex] AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(9 -(-9))^2 + (1 - 4)^2} [/tex]
[tex] = \sqrt{(18)^2 + (-3)^2} [/tex]
[tex] = \sqrt{(324 + 9} = \sqrt{333} [/tex]
[tex] AD = 18.2 units [/tex] (nearest tenth)
✍️Distance between B(-4, -3) and C(2, -4):
[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2 -(-4))^2 + (-4 -(-3))^2} [/tex]
[tex] = \sqrt{(6)^2 + (-1)^2} [/tex]
[tex] = \sqrt{(36 + 1} = \sqrt{37} [/tex]
[tex] BC = 6.1 units [/tex] (nearest tenth)
✍️Distance between B(-4, -3) and E(-3, 3):
[tex] BE = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3 -(-4))^2 + (3 -(-3))^2} [/tex]
[tex] = \sqrt{(1)^2 + (6)^2} [/tex]
[tex] = \sqrt{(1 + 36} = \sqrt{37} [/tex]
[tex] BE = 6.1 units [/tex] (nearest tenth)
✔️Area of the trapezoid:
Area = ½×(AD + BC)×BE
Plug in the values into the formula
Area = ½×(18.2 + 6.1)×6.1
Area = ½×(24.3)×6.1
Area = 74.115 ≈ 74.1 units² (nearest tenth)
