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Parallelogram Word Problems

Parallelogram Word Problems
  • Page 1
 1.  
What is the perimeter of ΔAED, if the area of the parallelogram ABCD is 24 cm2?

a.
12 cm
b.
15 cm
c.
30 cm
d.
10 cm


Solution:

= AB × DE
Area of the parallelogram ABCD = base × height

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

Height = DE = areaAB
= 246 = 4

Perimeter of ΔAED = AD + DE + AE

AE = 6 - 3 = 3 cm
AE = AB - BE
[Substitute AB = 6 and BE = 3.]

AD2 = 42 + 32
ADE is a right triangle, so AD2 = DE2 + AE2
[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


Solution:

Let h be the height of the triangle and b be the base of the triangle.

The area of the triangle = 1 / 2 × b × h

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

The new base is 2 × b and the new height is 2 × h.

The new area of the triangle = 1 / 2 × (2 × b) × (2 × h)

= 4 × (1 / 2 × b × h)

= 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 in2.
c.
34 in.
d.
13 in.


Solution:

Let b be the length of the base of the parallelogram as well as the rectangle.

Area of the parallelogram = 4 × b = 52
[Substitute the value of area of the parallelogram.]

Length of the base b = 13 in.
[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.


Solution:

Perimeter of a triangle is sum of its side lengths.

Let side lengths of a triangle be x units, y units, and z units.

Perimeter of the triangle = (x + y + z) units

If each side length were doubled then the sides will be 2x units, 2y units, 2z units.

New perimeter of the triangle = (2x + 2y + 2z) units = 2(x + y + z) units = 2 × original perimeter of the triangle.

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.


Solution:

From the figure, base of the triangle = 11 in.
      height of the triangle = 7 in.

Area of the triangle = 12 × base × height = 12 × 11 in. × 7 in. = 38.5 in.2

New height of the triangle = 4 in.

New area of the triangle = 12 × 11 in. × 4 in. = 22 in.2

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 m2. 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


Solution:

Area of the square = 64 m2
[Given.]

Side of the square = 64

= 8 m

Area of the square is increased by 4 times.
[Given.]

= 64 × 4

= 256 m2

Side of the square = 256

= 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


Solution:

The length of a cube is 4 m.

Volume of the cube = l3
[Formula.]

= 4 × 4 × 4 = 64 m3

Volume of the cube is increased by 8 times.
[Given.]

= 64 × 8 = 512 m3

Length of a cube = 5123

= 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


Solution:

The length and breadth of a rectangle are 5 cm and 6 cm.
[Given.]

Area of the rectangle = length × breadth.
[Formula.]

= 5 cm × 6 cm = 30 cm2
[Substitute the values.]

Area is increased by 4 times.
[Given.]

= 30 × 4 = 120 cm2

New length, l × 6 = 120
[Given breadth remains same.]

l = 120 / 6= 20 cm

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


Solution:

Perimeter of the parallelogram ABCD = AB + BC + CD + AD
[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


Solution:

The area of a parallelogram = base × height

= 10 × 7 = 70

So, the area of the parallelogram is 70 in.2.


Correct answer : (4)

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