Sort the following polygons in order of increasing perimeter.(1 point)
a square with vertices (7,2), (4,2,),(4,-1).(7,-1)
a rectangle with vertices (9,11), (8,11), (8,7), (9,7)
a triangle with vertices (-6,-5), (-2,-5), (-2,2)
To find the perimeter of a polygon, we need to calculate the distance between its vertices and sum them up.
a square with vertices (7,2), (4,2),(4,-1), and (7,-1):
Side 1: Distance between (7,2) and (4,2) = |7-4| + |2-2| = 3 + 0 = 3
Side 2: Distance between (4,2) and (4,-1) = |4-4| + |2-(-1)| = 0 + 3 = 3
Side 3: Distance between (4,-1) and (7,-1) = |4-7| + |-1-(-1)| = 3 + 0 = 3
Side 4: Distance between (7,-1) and (7,2) = |7-7| + |-1-2| = 0 + 3 = 3
Perimeter of the square = 3 + 3 + 3 + 3 = 12
a rectangle with vertices (9,11), (8,11), (8,7), and (9,7):
Side 1: Distance between (9,11) and (8,11) = |9-8| + |11-11| = 1 + 0 = 1
Side 2: Distance between (8,11) and (8,7) = |8-8| + |11-7| = 0 + 4 = 4
Side 3: Distance between (8,7) and (9,7) = |8-9| + |7-7| = 1 + 0 = 1
Side 4: Distance between (9,7) and (9,11) = |9-9| + |7-11| = 0 + 4 = 4
Perimeter of the rectangle = 1 + 4 + 1 + 4 = 10
a triangle with vertices (-6,-5), (-2,-5), and (-2,2):
Side 1: Distance between (-6,-5) and (-2,-5) = |-6-(-2)| + |-5-(-5)| = 4 + 0 = 4
Side 2: Distance between (-2,-5) and (-2,2) = |-2-(-2)| + |-5-2| = 0 + 7 = 7
Side 3: Distance between (-2,2) and (-6,-5) = |-2-(-6)| + |2-(-5)| = 4 + 7 = 11
Perimeter of the triangle = 4 + 7 + 11 = 22
So, the polygons in increasing order of perimeter are: the rectangle, the square, and the triangle.