﻿ Area of Squares and Rectangles Worksheet | Problems & Solutions

# 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.]

[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

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.

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.

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.]

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.

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.]

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.]

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.]

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.]

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.]