Perimeters of similar figures
Key Notes :
The following proportion applies to similar shapes:
a/b=p1/p2
where a/b is the ratio of the corresponding side lengths, and p1/p2 is the ratio of the perimeters.
Learn with an example
The figures below are similar. The labelled sides are corresponding.
What is the perimeter of the smaller hexagon?
P2 = _________ millimetres
Find the ratio of the corresponding side lengths.
a / b = 8/4 =2/1
Find the ratio of the perimeters.
p1 / p2 = 48 / p2
Use these two ratios to set up a proportion and solve for P2.
2 / 1 = 48 / p2
2 / 1 (p2) = 48 / p2 (p2) Multiply both sides by P2
2 p2 = 48 .1 Simplify
2 p2 = 48 Simplify
2 p2 ÷ 2= 48 ÷ 2 Divide both sides by 2
p2 = 24
The perimeter of the smaller hexagon is 24 millimetres.
The figures below are similar. The labelled sides are corresponding.
What is the perimeter of the smaller rectangle?
P1 = _________ millimetres
Find the ratio of the corresponding side lengths.
a / b = 2/6 =1/3
Find the ratio of the perimeters.
p1 / p2 = p1 / 30
Use these two ratios to set up a proportion and solve for p1.
1 / 3 = p1 / 30
1 / 3 (3 . 30) = p1 / 30 (3 . 30) Multiply both sides by 3 . 30
1 .30 = 3 p1 Simplify
30 = 3 p1 Simplify
30 ÷ 3= 3 p1 ÷ 3 Divide both sides by 3
10 = p1
The perimeter of the smaller rectangle is 10 centimetres.
The figures below are similar. The labelled sides are corresponding.
What is the perimeter of the smaller pentagon?
P2 = _________ millimetres
Find the ratio of the corresponding side lengths.
a / b = 9/5
Find the ratio of the perimeters.
p1 / p2 = 45 / p2
Use these two ratios to set up a proportion and solve for P2.
9 / 5 = 45 / p2
9 / 5 ( 5p2) = 45 / p2 (5p2) Multiply both sides by 5p2
9 p2 = 45 .5 Simplify
9 p2 = 225 Simplify
9 p2 ÷ 9 = 225 ÷ 9 Divide both sides by 9
p2 = 25
The perimeter of the smaller pentagon is 25 millimetres.
Let’s practice!
