Parallelogram Word Problems

**Page 1**

1.

What is the perimeter of ΔAED, if the area of the parallelogram ABCD is 24 cm^{2}?

a. | 12 cm | ||

b. | 15 cm | ||

c. | 30 cm | ||

d. | 10 cm |

Area of the parallelogram ABCD = base × height

24 = 6 × DE

[Substitute area of the parallelogram = 24 and DC = AB = 6.]

Height = DE =

=

Perimeter of ΔAED = AD + DE + AE

AE = 6 - 3 = 3 cm

AE = AB - BE

[Substitute AB = 6 and BE = 3.]

AD

ADE is a right triangle, so AD

[Substitute DE = 4 and AE = 3.]

= 16 + 9 = 25

[Simplify.]

AD = 5 cm

[Take square root on both sides]

So, perimeter of ΔADE = 5 + 4 + 3 = 12 cm

[Substitute the values of AD, DE and AE.]

Correct answer : (1)

2.

By how many times will the area of a triangle increase, if the base and the height are increased by 2 times?

a. | 2 times | ||

b. | 4 times | ||

c. | 4 times | ||

d. | 2 times |

The area of the triangle =

The length of the base and the length of the height are increased by 2 times.

The new base is 2 ×

The new area of the triangle =

= 4 × (

= 4 × original area of the triangle

The area of the triangle increases by 4 times.

Correct answer : (2)

3.

The area of a parallelogram is 52 in.^{2} and its altitude is 4 in. What is the perimeter of a rectangle of equal area standing on the same base?

a. | 52 in | ||

b. | 52 in ^{2}. | ||

c. | 34 in. | ||

d. | 13 in. |

Area of the parallelogram = 4 ×

[Substitute the value of area of the parallelogram.]

Length of the base

[Divide each side by 4.]

Base length of the rectangle = Base length of the parallelogram = 13 in.

Since the parallelogram and the rectangle have equal base and the area, the height of the parallelogram is equal to the width of the rectangle.

Width of the rectangle = 4 in.

Perimeter of the rectangle = 2 × (length + width)

= 2 × (13 + 4) = 2 × 17 = 34

[Substitute and simplify.]

The perimeter of the rectangle is 34 in.

Correct answer : (3)

4.

Perimeter of a triangle is 21 inches. If each side length were doubled, what would be the triangle′s new perimeter?

a. | 84 in. | ||

b. | 63 in. | ||

c. | 42 in. | ||

d. | 10.5 in. |

Let side lengths of a triangle be

Perimeter of the triangle = (

If each side length were doubled then the sides will be 2

New perimeter of the triangle = (2

Therefore, if each side length were doubled, then the triangle′s new perimeter will be two times the original perimeter of the traingle.

Triangle′s new perimeter = 2 × 21 in. = 42 in.

[Original perimeter of the triangle = 21 in.]

Correct answer : (3)

5.

If the height of the triangle in the figure is decreased to 4 in., what happens to the area of the triangle?

a. | It is decreased from 38.5 to 22 square inches. | ||

b. | It is decreased from 99 to 44 square inches. | ||

c. | It is decreased from 99 to 22 square inches. | ||

d. | It is decreased from 77 to 44 square inches. |

height of the triangle = 7 in.

Area of the triangle =

New height of the triangle = 4 in.

New area of the triangle =

If the height of the triangle in the figure is decreased to 4 in., then area of the triangle decreased from 38.5 to 22 square inches.

Correct answer : (1)

6.

The area of a square is 64 m^{2}. If the area of the square is increased by 4 times, what will be the change in the length of the side of the new square formed?

a. | length is tripled | ||

b. | length remains the same | ||

c. | length is halved | ||

d. | length is doubled |

[Given.]

Side of the square =

= 8 m

Area of the square is increased by 4 times.

[Given.]

= 64 × 4

= 256 m

Side of the square =

= 16 m.

The length of the side of the new square formed is doubled.

Correct answer : (4)

7.

The length of a cube is 4 m. If the volume of the cube is increased by 8 times, what will be the change in length of the side of the new cube formed?

a. | length is tripled | ||

b. | length is doubled | ||

c. | length is halved | ||

d. | length remains same |

Volume of the cube = l

[Formula.]

= 4 × 4 × 4 = 64 m

Volume of the cube is increased by 8 times.

[Given.]

= 64 × 8 = 512 m

Length of a cube =

= 8 m.

Length of the side of the new cube formed is doubled.

Correct answer : (2)

8.

The length and the breadth of a rectangle are 5 cm and 6 cm respectively. If the area of the rectangle is increased by 4 times with the breadth remaining the same, then find the change in the length of the rectangle.

a. | length increases by 2 | ||

b. | length increases by 3 | ||

c. | length increases by 4 | ||

d. | length increases by 6 |

[Given.]

Area of the rectangle = length × breadth.

[Formula.]

= 5 cm × 6 cm = 30 cm

[Substitute the values.]

Area is increased by 4 times.

[Given.]

= 30 × 4 = 120 cm

New length,

[Given breadth remains same.]

The length of the new rectangle formed increases by 4 times.

Correct answer : (3)

9.

Find the perimeter of the parallelogram ABCD.

a. | 18 cm | ||

b. | 16 cm | ||

c. | 22 cm | ||

d. | 24 cm |

[Sum of all the 4 sides.]

AB = DC = 4 cm and AD = BC = 5 cm

[Since ABCD is a parallelogram, AB = DC and BC = AD .]

Perimeter = 4 + 5 + 4 + 5 = 18 cm

[Substitue the values and add.]

Correct answer : (1)

10.

Find the area of a parallelogram, if the base is 10 inches and the corresponding height is 7 inches.

a. | 70 in. | ||

b. | 35 in. | ||

c. | 35 in. ^{2} | ||

d. | 70 in. ^{2} |

= 10 × 7 = 70

So, the area of the parallelogram is 70 in.

Correct answer : (4)