a The perimeter is the sum of the triangle's sides. The area is the product of its base and height divided by 2.
B
b To increase a shape by a scale factor of 3, we have to multiply each side's length by 3.
C
c Divide the perimeter of the image with the perimeter of the preimage. The quotient is called the linear scale factor.
D
d Divide the area of the image with the area of the preimage. This quotient is called the area scale factor.
A
aPerimeter: 23.4 meters
Area: 10.5 m^2
B
bPerimeter: 70.2 meters
Area: 94.5 m^2
C
c Yes.
D
d No, see solution.
Practice makes perfect
a The perimeter of a polygon is the sum of its sides. Examining the diagram, we notice that all sides are known. With this information we can calculate the perimeter.
Perimeter: 5+11.4+7=23.4 m
To find the triangle's area, we have to multiply its base and height and divide the product by 2. We have also been given this information.
Having identified the height and base, we can determine the area.
Now we can determine the perimeter and area using the same process as in Part A.
Perimeter:& 15+34.2+21=70.2 m
Area:& 1/2(21)(9)=94.5 m^2
c If the perimeter increases by a scale factor of 3, the ratio of the image perimeter to the preimage perimeter should equal 3. Let's test this.
70.2/23.4=3
The ratio between the perimeter of the image and the preimage does equal 3. When comparing perimeters of similar figures, this ratio is called the linear scale factor.
d Like in Part C, we will examine the ratio between the image area to the preimage area. This is called the area scale factor.
94.5/10.5=9
The scale factor between the areas is 9 and not 3. In fact, when comparing the areas of two similar figures, it will always be the square of the linear scale factor. From Part C, we know that the linear scale factor is 3. This means the area scale factor should be 3^2=9, which is the case.
