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 |

All the triangles are right triangles.

Δ SDC

[QB = SD, SC = QA, SAS postulate.]

Δ PAD

[PA = RC, PD = RB, SAS postulate.]

Area of ABCD = 46 × 30 - 2 (

= 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 |

[Area of the rectangle = length × width.]

Area of square is 30 × 30 = 900 cm

[Area of the square = side × side.]

So, both the areas are equal.

Correct answer : (3)

3.

The floor area of a room is 104 ft^{2}. 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 |

[Area of the square = side × side.]

Area of the two rectangular tiles = (6 × 4) + (6 × 4) = 48 ft

[Area of the rectangle = length × width.]

Total area = 50 + 48 = 98 ft

But the floor area of the room is 104 ft

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 cm ^{2} | ||

b. | 128 cm ^{2} | ||

c. | 256 cm ^{2} | ||

d. | 1024 cm ^{2} |

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

Area of the chess board = 64 × area of each square = 64 × 16 = 1024 cm

[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 cm ^{2} | ||

b. | 8 cm ^{2} | ||

c. | 16 cm ^{2} | ||

d. | 20 cm ^{2} |

[From the figure.]

So, the area of contact = 2 × 2 = 4 cm

Correct answer : (1)

6.

The perimeter of a square is 11.6 cm. What is the area of the square?

a. | 8.41 cm ^{2} | ||

b. | 134.56 cm ^{2} | ||

c. | 18.41 cm ^{2} | ||

d. | 46.4 cm ^{2} |

[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 cm

[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 |

[ Formula for area of the square.]

S

[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 |

[Given.]

Let the width =

[Given.]

Perimeter of the rectangle = 2 (

[Perimeter formula.]

Þ 2 (3

[Length + width = 3

Width =

Length = 2 × 7 = 14 cm

[Length = 2

Area = 14 × 7 = 98 cm

[Area of the rectangle is

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 |

[Given.]

Area =

[For rectangle.]

Length = 7 cm

[Given.]

Width =

Perimeter = 2(

[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 cm ^{2} | ||

b. | 76.88 cm ^{2} | ||

c. | 38.44 cm ^{2} | ||

d. | 29.22 cm ^{2} |

[Given.]

If

[Relation between side and a diagonal of the square.]

Therefore,

Area =

[Simplify.]

Correct answer : (1)