Question

Plot the points in the coordinate plane. Then find the perimeter and area of the polygon.

A(-3,5), B(1,6), C(3,-2), D(-1,-3)

Perimeter___________

Area__________________​

Answer 1

The answer to your question is below

Explanation:

See the graph below

Process

1.- Find the distance from A to B, B to C, C to D, A to D

Formula

d =
`\sqrt{(x2 - x1)^(2) + (y2 - y1)^(2)}`

d AB =
`\sqrt{(1 + 3)^(2) + (6 - 5)^(2)}  = √(17)`

dBC =
`\sqrt{(-2 -6)^(2) + (3 - 1)^(2)}  = √(68)`

dCD =
`\sqrt{(-1 - 3)^(2) + (-3 +2)^(2)}  = √(17)`

dAD =
`\sqrt{(-1 + 3)^(2) + (-3 - 5)^(2)}  = √(68)`

2.- Find the perimeter

Perimeter = 2
`√(17) + 2√(68)` =
`6√(17)` u

3.- Find the area

Area =
`√(17) x √(68)`

Area =
`√(17x68) = √(1156) = 34 u^(2)`