Area and Perimeter Word Problems

**Page 4**

31.

Find the perimeter of the shaded region in the parallelogram ABCD.

a. | 12 cm | ||

b. | 18 cm | ||

c. | 11 cm | ||

d. | 15 cm |

From the figure, BC = 5 cm, BE = 3 cm, AB = 7 cm, and DE = 3 cm.

EC = DC - DE = AB - DE = 7 - 3 = 4 cm.

[Lengths of the parallel sides in a parallelogram are equal, AB = DC.]

Perimeter of the ΔBEC = BC + CE + EB

[Formula.]

= 5 + 4 + 3

(Substitute the values)

= 12

[Add.]

So, the perimeter of the shaded region of the figure is 12 cm.

Correct answer : (1)

32.

Find the perimeter of the figure.

a. | 12.5 in. | ||

b. | 14.7 in. | ||

c. | 17.7 in. | ||

d. | 15.7 in. |

Perimeter of a figure = sum of all the sides of the figure

[Formula.]

Perimeter of the figure = AC + CD + DB + BA

= 5.2 + 2.5 + 2 + 5

[Substitute the values.]

= 14 .7

[Add.]

So, the perimeter of the figure is 14.7 in.

Correct answer : (2)

33.

What is the area of the triangle?

a. | 11.5 square units | ||

b. | 1.5 square units | ||

c. | 4.5 square units | ||

d. | 5 square units |

Height of the triangle = 3 units.

Area of a triangle with base

=

[Substitute the values.]

= 4.5

[Simplify.]

So, the area of the triangle is 4.5 square units.

Correct answer : (3)

34.

What is area of the shaded region?

a. | 105 in. ^{2} | ||

b. | 120 in. ^{2} | ||

c. | 95 in. ^{2} | ||

d. | None of the above |

Area of the triangle =

[Formula.]

=

[Substitute the values.]

= 105 in.

[Simplify.]

Area of the shaded region in the figure = 105 in.

Correct answer : (1)