Question

What is the area of trapezoid ABCD ? Enter your answer as a decimal or whole number in the box. Do not round at any steps. units²

Answer 1

37.5 is the answer :) I just took the quiz

Answer 2

37.5 sq. units.

Explanation:

The coordinate of vertices of trapezoid ABCD are given,

From the diagram it is clear the area of ABCD =
`(1)/(2)* AB * (AD + BC)` {Since, AD ║ BC and AB is the perpendicular distance between the parallel lines }

Now, AB =
`\sqrt{(- 3 - 1)^(2)+ (2 - 5)^(2)  } = 5` units

AD =
`\sqrt{(- 3 - 0)^(2)+ (2 - (-2))^(2)  } = 5` units

Again, BC =
`\sqrt{(1-7)^(2)+ (5 - (-3))^(2)  } = 10` units

Therefore, the area of trapezoid ABCD =
`(1)/(2) (10 + 5) * 5 = 37.5` sq. units. (Answer)

We know, that the distance formula between two points
`(x_(1), y_(1))` and
`(x_(2), y_(2))` is

`\sqrt{(x_(1) - y_(1) )^(2) + (x_(2) - y_(2) )^(2)  }`.