Area and Perimeter Word Problems

**Page 1**

1.

What is the area of a parallelogram, if its base is 9 ft and its height is 14 ft?

a. | 46 ft ^{2} | ||

b. | 126 ft ^{2} | ||

c. | 46 ft | ||

d. | 63 ft ^{2} |

[Formula.]

= 9 × 14

[Substitute the values of base and height.]

= 126

[Multiply.]

So, area of the parallelogram is 126 ft

Correct answer : (2)

2.

Find the area of the colored region in the figure.

a. | 22 cm ^{2} | ||

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

c. | 28 cm ^{2} | ||

d. | 26 cm ^{2} |

The base length of the parallelogram BEDF = 7 cm

[From the figure.]

The height of the parallelogram BEDF = 4 cm

[From the figure.]

Area of the parallelogram BEDF = base x height

[Formula.]

= 7 x 4

[Substitute the values.]

= 28

So, area of the colored region = area of the parallelogram BEDF = 28 cm

Correct answer : (3)

3.

What is the area of ΔABC in the figure, if the height of ΔABC is 3 times the height of ΔDBC and area of ΔDBC is 40 inch^{2}?

a. | 115 inch ^{2} | ||

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

c. | 110 inch ^{2} | ||

d. | None of the above |

[Formula.]

Let

Area of ΔDBC =

Height of ΔABC = 3 times the height of ΔDBC = 3

Area of ΔABC =

= 3 x (

= 3 x (Area of ΔDBC)

Area of ΔABC = 3 x 40 = 120 inch

Correct answer : (2)

4.

The perimeter of an equilateral triangle is 36 yd. What is the length of each side of the triangle?

a. | 108 yd | ||

b. | 12 yd | ||

c. | 3 yd | ||

d. | 9 yd |

So, the perimeter of an equilateral triangle = 3 × measure of each side.

36 = 3 × measure of each side

[Substitute the values.]

[Divide each side by 3.]

12 = measure of each side

[Simplify.]

So, the measure of each side of the equilateral triangle is 12 yd.

Correct answer : (2)

5.

Which of the figures have equal areas?

a. | Figure 1 & 3 | ||

b. | Figure 1 & 2 | ||

c. | Figure 2 and 3 | ||

d. | Figure 1,2 & 3 |

Area of the parallelogram = base × height = 4 × 2 = 8 square units.

Figure 2 represents a rectangle of length 4 units and width 2 units.

Area of the rectangle = length × width = 4 × 2 = 8 square units.

Figure 3 represents a triangle with a base length of 6 units and a height of 3 units.

Area of the triangle =

So, the parallelogram in figure 1 and the rectangle in figure 2 have equal areas.

Correct answer : (2)

6.

John spent $\frac{2}{3}$ of an hour watching a movie and $\frac{1}{6}$ of an hour cleaning his room. What fraction of an hour did he spend in both watching the movie and cleaning his room?

a. | $\frac{3}{9}$ | ||

b. | $\frac{1}{3}$ | ||

c. | $\frac{2}{3}$ | ||

d. | $\frac{5}{6}$ |

Correct answer : (4)

7.

Which two parallelograms have same area but different perimeters?

a. | Figure 1 and Figure 2 | ||

b. | Figure 2 and Figure 4 | ||

c. | Figure 1 and Figure 3 | ||

d. | Figure 3 and Figure 4 |

Area = 5 × 4 = 20 sq.units Perimeter = 2 × (5 + 4) = 18 units

Area = 6 × 3 = 18 sq.units Perimeter = 2 × (6 + 3) = 18 units

Area = 6 × 2 = 12 sq.units Perimeter = 2 × (6 + 2) = 16 units

Area = 4 × 3 = 12 sq.units Perimeter = 2 × (4 + 3) = 14 units

Therefore, parallelograms in Figure 3 and Figure 4 have same area but different perimeters.

Correct answer : (4)

8.

Which statement about the figures is true?

a. | Both the figures have the same area. | ||

b. | Both the figures have the same length. | ||

c. | Both the figures have the same perimeter. | ||

d. | Both the figures have the same width. |

Parallelogram in Figure 2 has a base of 4 units and a height of 3 units.

Area of a parallelogram = Base × Height Perimeter of a parallelogram = 2 × (Base + Height)

Area = 6 × 2 = 12 sq.units Perimeter = 2 × (6 + 2) = 16 units

Area = 4 × 3 = 12 sq.units Perimeter = 2 × (4 + 3) = 14 units

Therefore, the statement 'Both the figures have the same area' is true.

Correct answer : (1)

9.

Which of the following is true for a right triangle and a rectangle having equal bases and equal heights?

a. | The perimeter of the triangle is equal to the perimeter of the rectangle | ||

b. | The area of the triangle is equal to the area of the rectangle | ||

c. | The area of the triangle is half the area of the rectangle | ||

d. | The area of the rectangle is half the area of the triangle |

Let the length of the common height be

Area of the rectangle =

Area of the triangle =

=

So, the area of the triangle is half the area of the rectangle.

Correct answer : (3)

10.

A parallelogram and a rectangle have equal bases and equal heights. What is the area of the rectangle, if the area of the parallelogram is 44 cm^{2}?

a. | 44 cm ^{2} | ||

b. | 11cm ^{2} | ||

c. | 22 cm ^{2} | ||

d. | 88 cm ^{2} |

So, the area of the rectangle = the area of the parallelogram = 44 cm

Correct answer : (1)