a We have two different algebra tiles. The rectangular tiles have a dimension of x* 1 and the square tiles have sides of 1.
B
b We have three different kinds of tiles. The y^2-tiles have a dimension of y* y, the xy tiles have a dimension of x* y, and the squares have sides of 1.
A
aExpression: 2x+8
Sketch: See solution.
B
bExpression: 4y+2x+8
Sketch: See solution.
Practice makes perfect
a To determine the perimeter, we have to identify the length of the polygon's sides. Examining the diagram, we can identify two types of tiles. The rectangular tiles, with an area of x units^2 each, have a dimension of x* 1. With this information, we can label some of the polygon's sides.
We also have a smaller square tile with a side of 1. Let's add this information to the diagram.
We have one more side that is unknown. Notice that it is the difference between x and 1. At the same time, we will add up some of the units that are along the same side.
By adding the lengths around the polygon, we can determine the perimeter.
x+3+(x-1)+1+1+4 = 2x+8
b In this diagram, we have three different kinds of tiles.
c|c
Type & Dimension
xy & x* y
y^2 & y* y
square & 1* 1
Let's label some of the polygon's sides.
With this information, we can determine the length of the last few sides as well.
By adding the sides of the polygon, we can determine the perimeter. To simplify our calculations, we can first count the number of sides with the same length.
|c|c|c|
Length & Number of sides & Total length
y & 1 & y
x & 1 & x
1 & 12 & 12
x-1& 1 & 1(x-1)
y-1 & 3 & 3(y-1)
Finally, we will add the total length to determine the perimeter of the figure.
