Proportions and Similar Figures Worksheet

**Page 1**

1.

The area of a square is 32 m^{2}. Find the area of a similar square whose dimensions are quadrupled.

a. | 576 m ^{2} | ||

b. | 484 m ^{2} | ||

c. | 512 m ^{2} | ||

d. | 476 m ^{2} |

The ratio of area of the squares = 1

Therefore, area of bigger square = 16 × area of smaller square = 16 × 32 = 512 m

[Substitute and simplify.]

Correct answer : (3)

2.

Linda plays in a square-shaped ground beside their house, which has a side length of 24 m. She asks her dad to make a similar playing area in their house, whose area is $\frac{1}{16}$ of the area of the ground. What must be the side length of the new ground?

a. | 15 m | ||

b. | 6 m | ||

c. | 12 m | ||

d. | 3 m |

The ratio of areas of the grounds is 1 : 16 = 1

So, the ratio of the lengths of the grounds is 1 : 4

Therefore, length of the smaller square ground =

[Substitute and simplify.]

Correct answer : (2)

3.

The measure of each angle of a regular hexagon is 120°. A similar hexagon is formed by tripling the dimensions of the original hexagon. What will be the measure of each angle of the new hexagon?

a. | 240° | ||

b. | 120° | ||

c. | 108° | ||

d. | 60° |

Therefore, the measure of each angle of the new hexagon is 120°.

Correct answer : (2)

4.

A regular octagon measures 10 cm on each side. A similar octagon is formed by halving the side length of the original octagon. What will happen to the perimeter of the new octagon?

a. | perimeter does not change | ||

b. | perimeter triples | ||

c. | perimeter doubles | ||

d. | perimeter halves |

Perimeter of the original octagon = 8 × 10 = 80 cm

[Perimeter of an octagon = Number of sides × Length of each side.]

Side length of the new octagon =

[Side length of the new octagon is halved.]

Perimeter of the new octagon = 8 × 5 = 40 cm

=

So, perimeter of the new octagon is half the perimeter of the original octagon.

Correct answer : (4)

5.

The ratio of the areas of two regular hexagons is 1 : 36. Find the perimeter of the smaller hexagon, if the side length of the bigger hexagon is 12 cm.

a. | 6 cm | ||

b. | 36 cm | ||

c. | 1 cm | ||

d. | 12 cm |

The ratio of the areas is 1 : 36 = 1

Length of the smaller hexagon = Length of the bigger hexagon ×

So, the length of the smaller hexagon = 12 ×

[Substitute and simplify.]

Perimeter of the smaller hexagon = Length of the smaller hexagon × Number of sides of a hexagon = 2 × 6 = 12 cm

[Substitute and simplify.]

So, the perimeter of the smaller hexagon is 12 cm.

Correct answer : (4)

6.

The radii of two similar spheres are 12 cm and 18 cm. Find the ratio of their volumes.

a. | 8 : 27 | ||

b. | 3 : 4 | ||

c. | 27 : 8 | ||

d. | 2 : 3 |

[Given.]

Similarity ratio =

[Formula.]

=

The ratio of volumes of the spheres is

Correct answer : (1)

7.

Josh wants to make an advertisement board similar to another advertisement board, which has a length and width of 18 feet and 12 feet. He wants to have a length of 12 feet for the new board. What will be the width of the board that he wants to make?

a. | 10 feet | ||

b. | 8 feet | ||

c. | 9 feet | ||

d. | 7 feet |

[Write a proportion.]

[Write the cross products.]

[Divide both sides by 18.]

The width of the board that Josh wants to make, is 8 feet.

Correct answer : (2)

8.

Sam saw a house and built a model similar to the house. The height and width of the model are in the ratio of 1 : 3. If the width of the model is 9 feet, then what is the height of the model?

a. | 2 feet | ||

b. | 4 feet | ||

c. | 5 feet | ||

d. | 3 feet |

[Write a proportion]

1 × 9 = 3 ×

[Write a cross product.]

3 =

[Simplify.]

The height of the model is 3 feet.

Correct answer : (4)

9.

A regular hexagon measures 9 cm on each side. A similar hexagon is formed by halving the side length of the original one. What will happen to perimeter of the new hexagon?

a. | becomes four times the perimeter of the original hexagon | ||

b. | becomes half the perimeter of the original hexagon | ||

c. | becomes two times the perimeter of the original hexagon | ||

d. | perimeter does not change |

Perimeter of the original hexagon = 6 × 9 = 54 cm

[Perimeter of an hexagon = Number of sides × Length of each side.]

Side length of the new hexagon =

[Side length of the new hexagon is halved.]

Perimeter of the new hexagon = 6 × 4.5 = 27 cm

=

So, perimeter of the new hexagon becomes half the perimeter of the original hexagon.

Correct answer : (2)

10.

The side length of a heptagon is given as 10 in. A similar heptagon is formed by multiplying the side length of the original one by 3. What will happen to perimeter of the new heptagon?

a. | perimeter does not change | ||

b. | becomes two times the perimeter of the original heptagon | ||

c. | becomes three times the perimeter of the original heptagon | ||

d. | becomes four times the perimeter of the original heptagon |

Perimeter of the original heptagon = 7 × 10 = 70 in.

[Perimeter of an heptagon = Number of sides × Length of each side.]

Side length of the new heptagon = 3 ×10 = 30 in.

[Side length of the new heptagon is multiplied by 3.]

Perimeter of the new heptagon = 7 × 30 = 210 in.

= 3(70) = 3(Perimeter of the original heptagon)

So, perimeter of the new heptagon becomes three times the perimeter of the original heptagon.

Correct answer : (3)