a We can find the length of the horizontal and vertical sides by counting the number of steps they span in those directions.
B
b Multiply each side in the original figure by 3.
C
c Divide the larger figure's measurements by the smaller figures.
A
a Perimeter≈ 25.66 units
Area=34 units^2
B
bDiagram:
Perimeter ≈ 76.97 units
Area=306 units^2
C
cRatio of Perimeter: 3
Ratio of Area: 9
Practice makes perfect
a Let's find the area and perimeter one at the time.
Perimeter
To find the perimeter, we need to know the length of the shape's sides. We can find the length of the horizontal and vertical sides by counting the number of steps they span in those directions.
To find the last side we will add two segments, creating a right triangle.
By adding the sides of the shape we can find the perimeter.
5+2+3+4+4+sqrt(32)+2≈ 25.66 units
Area
To calculate the area we divide the shape into two rectangles and one triangle.
To calculate the triangle's area, we need its base and height. To calculate the rectangle's area we need their width and length. From the diagram we see that we know all of these dimensions, so we can find the shape's area by adding these products.
1/2(4)(4)+(5)(2)+(4)(4)=34 units^2
b To enlarge the figure so that the linear scale factor is 3, we have to multiply the length of each side by 3.
2(3)&=6 units
3(3)&=9 units
4(3)&=12 units
5(3)&=15 units
sqrt(32)(3)&=3sqrt(32) units
Now we can draw the enlarged figure.
When we know the shape's dimensions we can calculate its perimeter and area.
15+6+9+12+12+12sqrt(2)+6&≈ 76.97 units
1/2(12)(12)+(15)(6)+(12)(12)&=306 units^2
c To calculate the ratio of the shapes' perimeters and areas, we divide the bigger shape's measurements with the smaller shapes.
