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Area and Perimeter Word Problems - Page 2

Area and Perimeter Word Problems
  • Page 2
 11.  
The height of a parallelogram is twice its base. What are the measures of the base and the height, if the area of the parallelogram is 288 m2?
a.
6 m and 12 m
b.
24 m and 48 m
c.
12 m and 24 m
d.
12 m and 36 m


Solution:

Let b be the base of the parallelogram.

Height of the parallelogram = Twice that of the base = 2b

Area of the parallelogram = base × height
[Formula.]

288 = b × 2b
[Substitute the values.]

144 = b2

144 = b2, b = 12
[Taking square root on both sides.]

Base of the parallelogram = 12 m

Height of the parallelogram = 2b = 2(12) = 24 m

Therefore, the base and height of the parallelogram are 12 m and 24 m respectively.


Correct answer : (3)
 12.  
What is the height of the parallelogram, if the base is half of its height and its area is 128 cm2?
a.
13 cm
b.
14 cm
c.
26 cm
d.
16 cm


Solution:

Let h be the height of the parallelogram.

Base of the parallelogram = Half of the height = h2

The area of the parallelogram = base × height

128 = h2 × h
[Substitute the values.]

128 × 2 = h2
[Multiply each side by 2.]

16 = h
[Take square root on both the sides.]

Therefore, the height of the parallelogram is 16 cm.


Correct answer : (4)
 13.  
The state of Virginia is shaped like a triangle. If it has a base length of 406 miles and covers an area of about 40,980 square miles, what will be its height?

a.
about 202 miles
b.
about 406 miles
c.
about 812 miles
d.
about 101 miles


Solution:

Area of a triangle = 1 / 2 × base × height
[Formula.]

Area covered by the state of Virginia = 1 / 2 × 406 × h, where h is the height of the triangle.

1 / 2 × 406 × h = 40,980 h 202

So, the height of the triangle is about 202 miles.


Correct answer : (1)
 14.  
Find the area of the given parallelogram ABCD, if the area of the triangle ABE is 78 cm2.


a.
156 cm2
b.
78 cm2
c.
150 cm2
d.
39 cm2


Solution:

Area of a parallelogram = base × height
Area of a triangle = 1 / 2 × base × height

If the base and height of the parallelogram and the triangle are same then the area of the parallelogram is twice the area of the triangle.

Thus the area of the parallelogram ABCD = 2 × area of the triangle ABE

= 2 × 78 = 156
[Substitute the values.]

So, the area of the parallelogram ABCD is 156 cm2.


Correct answer : (1)
 15.  
Find the area of the triangle ABE, if the area of the parallelogram ABCD is 100 cm2.

a.
80 cm2
b.
50 cm2
c.
30 cm2
d.
90 cm2


Solution:

Area of a parallelogram = base × height
Area of a triangle = 1 / 2 × base × height

If the base and height of the parallelogram and the triangle are same then the area of the triangle is half of the area of the parallelogram.

Thus the area of the triangle ABE = 1 / 2 × area of the parallelogram ABCD

= 12 × 100 = 50
[Substitute the values.]

So, the area of the triangle ABE is 50 cm2.


Correct answer : (2)
 16.  
Find the area of rectangle PQRS, if the area of the triangle PQT is 80 in.2.

a.
140 in.2
b.
120 in.2
c.
160 in.2
d.
80 in.2


Solution:

Area of a rectangle = length × width
Area of a triangle = 1 / 2 × base × height

If the base and height of the rectangle and the triangle are same then the area of the rectangle is twice the area of the triangle.

Thus the area of the rectangle PQRS = 2 × area of the triangle PQT

= 2 × 80 = 160
[Substitute the values.]

So, the area of the rectangle PQRS is 160 in.2.


Correct answer : (3)
 17.  
Find the area of the parallelogram ABCD.


a.
13.5 cm2
b.
15 cm2
c.
15.5 cm
d.
32 cm


Solution:

Length of the base = 6 cm.
[Given.]

Area of the parallelogram = base length × height.
[Formula]

= 6 cm × 2.5 cm
[Substitute the respective values in the formula.]

= 15 cm2.

So, the area of the parallelogram ABCD is 15 cm2.


Correct answer : (2)
 18.  
What is the area of the shaded region in the figure?


a.
180 cm2
b.
120 cm2
c.
130 cm2
d.
None of the above


Solution:

From the figure, shaded region = ACD.

ACD is in triangular shape.

Area of the triangle ACD = 1 / 2 × base × height
[Formula.]

From the figure base of the triangle ACD = 15 cm and height = 16 cm.

The area of the triangle ACD = 1 / 2 × 15 × 16
[Substitute the values.]

120 cm2
[Simplify.]

The area of the triangle ACD = 120 cm2.


Correct answer : (2)
 19.  
What is the area of the triangle ABD in the figure, if the area of a parallelogram is 30 ft2?

a.
15 ft2
b.
20 ft2
c.
17 ft2
d.
None of the above


Solution:

If a parallelogram and the triangle have same base and same height then the area of the triangle is half of the area of the parallelogram.

From the figure, the parallelogram and the triangle have same base and same height.

The area of the triangle = 1 / 2 × area of the parallelogram

= 12× 30
[Since area of the parallelogram = 30.]

= 15
[Simplify.]

The area of the triangle = 15 ft2.


Correct answer : (1)
 20.  
What is the area of the parallelogram, if the area of the triangle is 22m2?.

a.
47 m2
b.
44 m2
c.
54 m2
d.
None of the above


Solution:

From the figure, the triangle and the parallelogram have same bases and the same heights.

The area of the parallelogram = 2 × area of the triangle.

= 2 × 22
[Substitute the area of triangle = 22.]

= 44

The area of the parallelogram = 44 m2.


Correct answer : (2)

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