Question

What is the area of a polygon with vertices of (-2, -4), (4, -4), (4, 4), and (-5, 4)?thank you ! :)

Answer 1

Given:

The vertices of the polygon are (-2, -4), (4, -4), (4, 4), and (-5, 4).

Required:

We need to find the area of the given polygon.

Step-by-step explanation:

Mark the points (-2, -4), (4, -4), (4, 4), and (-5, 4) and join them by line.

We get the polygons ABCD is a trapezoid.

BD is height of the trapezoid.

Let AB=a, CD=b, and BD=h.

Use the distance formula to find the measure of length.

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Consider the points (-5,4) and (4,4).

`Substitute\text{ }x_2=4,x_1=-5,y_2=4,\text{ and }y_1=4\text{ in the distance formula.}`

`a=√((4-(-5))^2+(4-4)^2)`
`a=√((4+5)^2+0)`
`a=√(9^2)`
`a=9units`

Consider the points (-2,-4) and (4,-4).

`Substitute\text{ }x_2=4,x_1=-2,y_2=-4,\text{ and }y_1=-4\text{ in the distance formula.}`

`b=√((4-(-2))^2+(-4-(-4))^2)`
`b=√((4+2)^2+(-4+4)^2)`
`b=√(6^2+0)`
`b=6units`

Consider the points (4,4) and (4,-4).

`Substitute\text{ }x_2=4,x_1=4,y_2=-4,\text{ and }y_1=4\text{ in the distance formula.}`

`h=√((4-4)^2+(-4-4)^2)`
`h=√(0+8^2)`
`h=8units`

Consider the area of the trapezoid formula.

`A=(a+b)/(2)h`

Substitute a = 9 units, b = 6 units, and h =8 units in the formula.

`A=(9+6)/(2)\cdot8`
`A=15\cdot4`
`A=60units^2`

Final answer:

The area of a polygon is 60 square units.