Question

What is the area of the trapezoid shown? trapezoid A = ______ units²?

Answer 1

74.1 units²

Explanation:

Area of the trapezoid shown = ½×(AD + BC)×BE

Use distance formula,
`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)` to find AD, BC, and BE.

✍️Distance between A(-9, 4) and D(9, 1):

`AD = √((x_2 - x_1)^2 + (y_2 - y_1)^2) = √((9 -(-9))^2 + (1 - 4)^2)`

`= √((18)^2 + (-3)^2)`

`= √((324 + 9) = √(333)`

`AD = 18.2 units` (nearest tenth)

✍️Distance between B(-4, -3) and C(2, -4):

`BC = √((x_2 - x_1)^2 + (y_2 - y_1)^2) = √((2 -(-4))^2 + (-4 -(-3))^2)`

`= √((6)^2 + (-1)^2)`

`= √((36 + 1) = √(37)`

`BC = 6.1 units` (nearest tenth)

✍️Distance between B(-4, -3) and E(-3, 3):

`BE = √((x_2 - x_1)^2 + (y_2 - y_1)^2) = √((-3 -(-4))^2 + (3 -(-3))^2)`

`= √((1)^2 + (6)^2)`

`= √((1 + 36) = √(37)`

`BE = 6.1 units` (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)