Question

Figure ABCD has vertices A(−6, 3), B(2, 3), C(2, −4), and D(−6, −1). What is the area of Figure ABCD?

Answer 1

Area of figure ABCD = 44 units square

Explanation:

Plotting the given points:

`A(-6,3)`,
`B(2,3)`,
`C(2,-4)` and
`D(-6,-1)`

On plotting the points we find out that the figure is a trapezoid with sides

`AD\parallel BC`

From the graph Length of parallel sides can be found out as they are vertical lines:

`AD=4\ units`

`BC=7\ units`

Length of a non parallel side AB can be found out as it is a horizontal line.

`AB=8\ units`

Note:
`AB\perp BC`, so
`AB` is the height of trapezoid as height is perpendicular distance between the parallel sides.

Area of trapezoid is given by

⇒
`(Sum\ of\ parallel\ sides)/(2) * height`

⇒
`((AD+BC)/(2))* AB`

⇒
`((4+7)/(2))* 8`

⇒
`44` units square

∴ Area of figure ABCD = 44 units square