Find the perimeter of the polygon with the vertices A (−1, 1), B (4, 1), C (4,−2), and D(−1,−2).
The perimeter of ABCD is ___ units.
Could someone explain how I can figure this out?
To find the perimeter of a polygon, you need to calculate the sum of the lengths of all its sides.
To calculate the length of a side, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is used to determine the distance between two points in a plane. It is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's use this formula to calculate the length of each side of the given polygon:
Side AB:
- Point A coordinates: (-1, 1)
- Point B coordinates: (4, 1)
Using the distance formula:
dAB = √((4 - (-1))^2 + (1 - 1)^2)
= √((5)^2 + (0)^2)
= √(25)
= 5 units
Side BC:
- Point B coordinates: (4, 1)
- Point C coordinates: (4, -2)
Using the distance formula:
dBC = √((4 - 4)^2 + (-2 - 1)^2)
= √((0)^2 + (-3)^2)
= √(9)
= 3 units
Side CD:
- Point C coordinates: (4, -2)
- Point D coordinates: (-1, -2)
Using the distance formula:
dCD = √((-1 - 4)^2 + (-2 - (-2))^2)
= √((-5)^2 + (0)^2)
= √(25)
= 5 units
Side DA:
- Point D coordinates: (-1, -2)
- Point A coordinates: (-1, 1)
Using the distance formula:
dDA = √((-1 - (-1))^2 + (1 - (-2))^2)
= √((0)^2 + (3)^2)
= √(9)
= 3 units
Now that we have the lengths of all four sides, we can sum them up to find the perimeter:
Perimeter = AB + BC + CD + DA
= 5 + 3 + 5 + 3
= 16 units
Therefore, the perimeter of polygon ABCD is 16 units.
A polygon has vertices at -(1, 1),(1,-1), and (-1,-1)
you could do a sketch
or use the distance formula four times
or look at coordinates
... the repetition of x and y values means vertical and horizontal lines
... this looks to be a rectangle