Area and Perimeter Word Problem Worksheets

**Page 1**

1.

The figure shows two regular pentagons which are similar. If the area of the larger pentagon is 45 cm^{2} then find the area of the shaded portion of the smaller pentagon. [Given $a$ = 8 and $b$ = 12.]

a. | 20 cm ^{2} | ||

b. | 27 cm ^{2} | ||

c. | 12 cm ^{2} | ||

d. | 8 cm ^{2} |

[Replace

If the ratio of the two similar figures is a : b then the ratio of their areas is

[Sides of two similar figures.]

Area of the larger pentagon = 45 cm

[Given.]

Let A be the area of smaller pentagon.

[From step 3 and step 4.]

A =

[Simplify.]

Area of shaded portion =

[Pentagon is divided into 5 congruent triangles.]

Correct answer : (4)

2.

The area of the smaller regular hexagon is 120 cm^{2}. Find the area of the shaded portion of larger regular hexagon if the two hexagons are similar. [Given $a$ = 6 and $b$ = 12.]

a. | 120 cm ^{2} | ||

b. | 240 cm ^{2} | ||

c. | 250 cm ^{2} | ||

d. | 480 cm ^{2} |

If the similarity ratio of the two similar figures is

[Two hexagons are similar.]

Area of the smaller hexagon = 120 cm

[Given.]

Let A be the area of larger hexagon.

[Write in proportion.]

A = 120 × 4 = 480

[Simplify.]

Area of the shaded region =

[3 parts are shaded.]

Correct answer : (2)

3.

Trapezoid ABCD is similar to trapezoid MNOP. Find the ratio of their areas. [Given $a$ = 8 units and $b$ = 14 units.]

a. | 7 : 4 | ||

b. | 16 : 49 | ||

c. | 4 : 7 | ||

d. | 49 : 16 |

[Given.]

If the similarity ratio of two similar figures is

[Substitute.]

[Trapezoid ABCD ~ Trapezoid MNOP.]

Therefore ratio of the areas = 16 : 49

Correct answer : (2)

4.

Two figures are similar if ______

a. | they have the same size but different shape | ||

b. | they have the different size and different shape | ||

c. | they have some portion in common | ||

d. | they have the same shape but not necessarily the same size |

Correct answer : (4)

5.

The area of trapezoid ABCD is 9 cm^{2} and trapezoid PQRS is 16 cm^{2}. If the two trapezoids are similar, then find the value of $x$. [Given AB = 4 cm and CD = 8 cm.]

a. | 6 cm | ||

b. | 8 cm | ||

c. | 16 cm | ||

d. | 2.67 cm |

[Given.]

[Given.]

If

[Simplify.]

Consider the sides AB and PQ.

Length of the side AB is 4 cm and let the length PQ be

[Given.]

[From step 5.]

[Simplify.]

Consider the sides CD and RS.

Length of the side CD is 8 cm and let the length RS be

[Given.]

[Simplify.]

[Formula.]

=

[From steps 9 and 13.]

=

Hence, the value of

Correct answer : (2)

6.

Two regular pentagons ABCDE and PQRST are similar. The length of a side of ABCDE is 5 cm. Find the length of a side of PQRST if its area is 16 times the area of ABCDE.

a. | 20 cm | ||

b. | 5 cm | ||

c. | 80 cm | ||

d. | 400 cm |

The two pentagons are similar.

[Given.]

If the ratio of corresponding sides of two similar figures is

[Pentagons are similar.]

[Area of pentagon PQRST = 16 × Area of pentagon ABCDE.]

[Cross - multiply.]

[Simplify.]

The length of each side of a pentagon is 20 cm.

Correct answer : (1)

7.

The circle R is similar to the circle S. The ratio of their radii is 2 : 3. If the area of the semicircle S is 9$\pi $ sq.units, then find the area of the semicircle with center R.

a. | 3$\pi $ sq.units | ||

b. | 9$\pi $ sq.units | ||

c. | 4$\pi $ sq.units | ||

d. | 2$\pi $ sq.units |

[Given.]

Area of the semicircle (S) = 9

[Given.]

Let the area of the semicircle (R) be

If the similarity ratio of two similar figures is

[

[From step 2.]

Area of the semicircle with center R = 4

Correct answer : (3)

8.

Franklin paid a carpenter $4 to polish his wooden table which is 12 ft long. His neighbour Samson has a similar wooden table of length 18 ft. How much Samson has to pay to have his wooden table polished by the same carpenter?

a. | $6 | ||

b. | $4 | ||

c. | $14 | ||

d. | $9 |

Length of Samson's wooden table = 18 ft

[Similarity ratio.]

If the similarity ratio of the two similar figures is

Cost of polishing is proportional to the area of the table.

[Write in proportion.]

[Simplify.]

Hence, Samson has to pay $9 to have his wooden table polished by the same carpenter.

Correct answer : (4)

9.

If the areas of two similar decagons are 81 ft^{2} and 225 ft^{2}, then find the ratio of their perimeters.

a. | 3 : 5 | ||

b. | 25 : 9 | ||

c. | 9 : 25 | ||

d. | 5 : 3 |

[Given.]

If the similarity ratio of two similar figures is

[From steps 1 and 2.]

[The ratio of the areas

[Simplify.]

3 : 5 is the similarity ratio.

[From step 2.]

The ratio of the perimeters is the same as the similarity ratio.

Hence, the ratio of their perimeters = 3 : 5

Correct answer : (1)

10.

A light $a$ m above the ground causes a boy $b$ m tall to cast a shadow $s$ meters long measured along the ground. Express $s$ interms of $d$, where $d$ is the distance between the boy and the base of the light in meters. [Given $a$ = 4, $b$ = 0.8.]

a. | $s$ = 4 $d$ | ||

b. | $s$ = 0.25 $d$ | ||

c. | $s$ = 4.8 $d$ | ||

d. | $s$ = 0.8 $d$ |

Draw the figure.

We can observe two similar triangles from the figure.

[Write the proportion.]

4

[Cross multiply.]

4

[Simplify.]

3.2

[Solve for

Correct answer : (2)

More Area and Perimeter Word Problem Worksheets | |

Area and Perimeter Word Problems | |