b The perimeter is the sum of the polygons' sides. To find the area of the polygons, you should divide them into a triangle and a rectangle.
A
aDiagram:
B
bPerimeter ABCDE: 28
Perimeter A'B'C'D'E': 56 Area ABCDE: 52 Area A'B'C'D'E': 208
Practice makes perfect
a We will begin by plotting ABCDE.
To enlarge the polygon by a factor of 2, we have to double the distance between each vertex and the origin in the same direction. We can do this if we multiply each point's coordinates by 2.
Point original
(x,y)
(2x,2y)
A
(- 3,- 2)
(- 6,- 4)
B
(5,- 2)
(10,- 4)
C
(5,3)
(10,6)
D
(1,6)
(2,12)
E
(- 3,3)
(- 6,6)
With this, we can plot the dilated polygon.
b The perimeter adds up the length of a figure's sides. Any horizontal and vertical parts are the easiest to measure. The length of a horizontal segment is the absolute value of the difference of the x-coordinates. Similarly, the length of a vertical segment is the absolute value of the difference of the y-coordinates.
To measure the distance of the remaining sides, we have to use the Distance Formula.
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
d
D( 1,6), E( - 3,3)
sqrt(( 1-( - 3))^2+( 6- 3)^2)
5
C( 5,3), E( 1,6)
sqrt(( 5- 1)^2+( 3- 6)^2)
5
D'( 2,12), E'( - 6,6)
sqrt(( 2-( - 6))^2+( 12- 6)^2)
10
C'( 10,6), E'( 2,12)
sqrt(( 10- 2)^2+( 6- 12)^2)
10
Let's mark the last sides length in the diagram.
Now we have enough information to calculate the perimeters of the polygons.
ABCDE:& 8+5+5+5+5=28
A'B'C'D'E':& 16+10+10+10+10=56
To find the area of the polygons, we will divide them into a rectangle and a triangle. Note that the area of a triangle is half it's base times it's height. Therefore, we will also mark the triangle heights.
Now we have enough information to calculate the area of the polygons.
ABCDE:& (8)(5)+1/2(8)(3)=52
A'B'C'D'E':& (10)(16)+1/2(16)(6)=208
