FINDING PERIMETER AND AREA OF SIMILAR FIGURES WORKSHEET

Problem 1 :

Triangle HIJ is similar to triangle STR, what is the perimeter of triangle STR

Solution

Problem 2 :

If the two triangles are similar

Find

i) Scale factor

ii) Ratio of perimeter

iii)  Ratio of area

Solution

Problem 3 :

Two triangles have a scale factor of 2/3. The area of the larger triangle is 12 cm2. What is the area of smaller triangle.

Solution

Problem 4 :

If the length of each side of triangle is cut to 1/3 of its original size, what happens to the area of the triangle ?

The new area is _______________ of the original area.

Solution

Problem 5 :

For the two triangles below to be similar, which of the following be true ?

a)  x = 2y/3    b)  c = 3y/2     c)  x = 3y     d)  x = y

Solution

Problem 6 :

An architect is building a model of a tennis court for a new client. On the model, the court is 6 inches wide and 13 inches long. An official tennis court is 36 feet wide. What is the length of a tennis court ?

Solution

Answer Key

1) Perimeter of STR = 37 

2)  

i) Scale factor = 3 : 1

ii)  Ratio of perimeter = 3 : 1

iii)  Ratio of area = 32 : 12

3)  5.3 cm2

4)  Area of smaller triangle = (1/9) of area of larger triangle.

5) x = 2y/3

6) 78 feet.

The figures in each pair are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Find the scale factor and the ratio of perimeters for each pair of similar figures.

Problem 4 :

Two regular octagons with areas 4 ft² and 16 ft²

Solution

Problem 5 :

Two trapezoids with areas 49 cm² and 9 cm²

Solution

Problem 6 :

Two equilateral triangles with areas 16√3 ft² and √3 ft²

Solution

Problem 7 :

Two circles with areas 2π cm² and 200π cm²

Solution

Answer Key

1)  Perimeter = 1 : 2, area = 1 : 4

2) Perimeter = 3 : 5, area = 9 : 25

3) Perimeter = 4 : 3, area = 16 : 9

4)  1 : 2

5)  7 : 3

6)  4 : 1

7)  1 : 100

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