Area of Squares and Rectangles Worksheet

Area of Squares and Rectangles Worksheet
  • Page 1
 1.  
Find the area of the figure ABCD enclosed in the rectangle PQRS with PQ = 46 cm, QR = 30 cm, SD = QB = 10 cm and PA = RC = 20 cm.


a.
1050 sq cm
b.
730 sq cm
c.
720 sq cm
d.
1215 sq cm


Solution:

Area of ABCD = Area of the rectangle - ( Area of Δ PAD + Area of Δ QAB + Area of Δ BCR + Area of Δ CDS)

All the triangles are right triangles.

Δ SDC Δ QBA
[QB = SD, SC = QA, SAS postulate.]

Δ PAD Δ RCB
[PA = RC, PD = RB, SAS postulate.]

Area of ABCD = 46 × 30 - 2 (1 / 2 × 26 × 10 + 1 / 2 × 20 × 20)

= 1380 - 2(130 + 200) = 720 sq cm


Correct answer : (3)
 2.  
Which of the following has larger area?
A rectangle of size 36 cm × 25 cm.
A square of side 30 cm.
a.
rectangle is larger
b.
square is larger
c.
both are same


Solution:

Area of rectangle is 36 × 25 = 900 cm2
[Area of the rectangle = length × width.]

Area of square is 30 × 30 = 900 cm2
[Area of the square = side × side.]

So, both the areas are equal.


Correct answer : (3)
 3.  
The floor area of a room is 104 ft2. Two square tiles of side 5 ft each and two rectangle tiles of 6 ft × 4 ft are available to floor the room. Does the tiles available are sufficient ?
a.
yes
b.
no


Solution:

Area of the two square tiles available = (5 × 5 ) + (5 × 5) = 50 ft2
[Area of the square = side × side.]

Area of the two rectangular tiles = (6 × 4) + (6 × 4) = 48 ft2
[Area of the rectangle = length × width.]

Total area = 50 + 48 = 98 ft2.

But the floor area of the room is 104 ft2. So the tiles available are not sufficient to cover the area.


Correct answer : (2)
 4.  
Find the area of a chess board with each black and white square having a side length of 4 cm. Chess board contains 8 squares in a row and 8 squares in a column.
a.
64 cm2
b.
128 cm2
c.
256 cm2
d.
1024 cm2


Solution:

Chess board contains 8 squares in a row and 8 squares in a column.

Total number of square in chess board is 8 × 8 = 64

Area of the chess board = 64 × area of each square = 64 × 16 = 1024 cm2
[Since area of each square = S × S.]


Correct answer : (4)
 5.  
Find the area of contact of the two rectangular blades which are exactly perpendicular to each other.

a.
4 cm2
b.
8 cm2
c.
16 cm2
d.
20 cm2


Solution:

The dimensions of the area of contact are 2 cm, 2 cm.
[From the figure.]

So, the area of contact = 2 × 2 = 4 cm2.


Correct answer : (1)
 6.  
The perimeter of a square is 11.6 cm. What is the area of the square?
a.
8.41 cm2
b.
134.56 cm2
c.
18.41 cm2
d.
46.4 cm2


Solution:

The perimeter of a square = 4 × Side.
[From formula of perimeter of square.]

4 × Side = 11.6 cm
[Given.]

Side = 2.90 cm
[Simplify.]

Area of the square = Side × Side = 2.90 × 2.90 = 8.41 cm2
[Area of the square = Side × Side.]


Correct answer : (1)
 7.  
The area of a square is 49 cm². What is the length of its side?
a.
7 cm
b.
12.25 cm
c.
11 cm
d.
28 cm


Solution:

Area of a square of side S is S2.
[ Formula for area of the square.]

S2 = 49 cm2.
[Given.]

Side of the square = S = 7 cm
[Solve for S.]


Correct answer : (1)
 8.  
The perimeter of a rectangle is 42 cm. The length of rectangle is 2 times its width. Find its area.
a.
196 cm²
b.
49 cm²
c.
98 cm²
d.
24.5 cm²


Solution:

Perimeter = 42 cm
[Given.]

Let the width = w = x, then length = l = 2x
[Given.]

Perimeter of the rectangle = 2 (l + w)
[Perimeter formula.]

Þ 2 (3x) = 42 Þ 6 x = 42
[Length + width = 3x.]

Width = x = 7 cm

Length = 2 × 7 = 14 cm
[Length = 2x.]

Area = 14 × 7 = 98 cm2
[Area of the rectangle is l × w.]


Correct answer : (3)
 9.  
The area of a rectangle is 14 cm², its length is 7 cm. What is its perimeter?
a.
36 cm
b.
9 cm
c.
18 cm
d.
14 cm


Solution:

Area = 14 cm².
[Given.]

Area = l × w.
[For rectangle.]

Length = 7 cm
[Given.]

Width = w = 14 / 7 = 2 cm.

Perimeter = 2(l + w)
[Formula for perimeter of rectangle.]

Perimeter = 2(7 + 2) = 18 cm
[Simplify.]


Correct answer : (3)
 10.  
The length of the diagonal of a square is 6.2 cm. Find the area.
a.
19.22 cm2
b.
76.88 cm2
c.
38.44 cm2
d.
29.22 cm2


Solution:

Length of diagonal = 6.2 cm.
[Given.]

If a is the side of a square, then the length of the diagonal is a2.
[Relation between side and a diagonal of the square.]

Therefore, a2 = 6.2 a = 6.22

Area = a2 = (6.22)2 = 38.44 / 2 = 19.22 cm2
[Simplify.]


Correct answer : (1)

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