Current Affairs 4th Class

Category : 4th Class

Measurement

Learning Objectives

• Perimeter
• Area

In previous chapter, we have studied about shapes based on their properties. Perimeter and area are important concepts in our daily life as they widely applied by builders, painters, farmers, and gardeners. Perimeter is the total length of the boundary of a closed shape whereas the space inside the closed shape is its area. In this chapter, we will learn how to estimate and find the perimeter and area of geometrical shapes.

1. A plane figure bounded by line segments and composed of angular corners is called a rectilinear figure. For examples, triangle, quadrilateral, hexagon, etc.

2. A circle is not a recti linear figure.

3. Length of the total boundary of a closed figure is called its perimeter.

4. Perimeter of a triangle is equal to the sum of the lengths of all its sides.

5. Perimeter of an equilateral triangle is thrice the length of its one side. Therefore, perimeter of equilateral triangle = \[3\times \text{side}\]

6. Perimeter of a rectangle is twice the sum of its length and breadth. Therefore, perimeter of rectangle = \[~2\times (\text{length}+\text{breadth)}\]

7. Perimeter of a square is four times the length of a side. Therefore, perimeter of square = \[4\times \text{side}\]

8. Area is the two-dimensional space covered by a surface. It is a measure of how much space is there on a flat surface.

9. Area of a rectangle is the product of its length and breadth. Therefore, area of rectangle = \[\text{length}\times \text{breadth}\]

10. Area of a square is the product of its any two sides. Therefore, area of square = \[\text{side}\times \text{side}\]

Example:

1. Amit wants new carpeting for his living room. His living room is a 8 m by 7 m rectangle. How much carpet does he need to buy to cover his entire living room?

(a) \[\text{64 }{{\text{m}}^{2}}\]                                

(b) \[\text{56 }{{\text{m}}^{2}}\]

(c) \[\text{49 }{{\text{m}}^{2}}\]                       

(d) \[\text{30 }{{\text{m}}^{2}}\]

(e) None of these

Answer (b) is correct.

Explanation: Here, length of the room = 8 m, and its breadth = 7 m

Therefore, the area of room = \[\text{length}\times \text{breadth}=(8\times 7)\text{ }{{\text{m}}^{2}}=56\text{ }{{m}^{2}}\]

Hence, Amit needs to buy \[\text{56 }{{\text{m}}^{2}}\] carpet to cover his entire living room.

2. A square garden with a side length of 120 m has a square swimming pool in very centre with a side length of 20 m. Calculate the area of the garden.

(a) \[14400\text{ }{{\text{m}}^{2}}\]                    

(b) \[25600\text{ }{{\text{m}}^{2}}\]

(c) \[10000\text{ }{{\text{m}}^{2}}\]                   

(d) \[14000\text{ }{{\text{m}}^{2}}\]

(e) None of these

Answer (d) is correct.

Explanation: Area of swimming pool = \[\text{side}\times \text{side}=(20\times 20)\text{ }{{\text{m}}^{2}}=400\text{ }{{\text{m}}^{2}}\]

Area of the garden including swimming pool = \[\text{side}\times \text{side}=(120\times 120)\text{ }{{\text{m}}^{2}}=14400\text{ }{{\text{m}}^{2}}\]

Therefore, area of garden = area of garden including swimming pool \[-\] area of swimming pool

= \[\text{(14400}-400)\text{ }{{\text{m}}^{2}}=14000\text{ }{{\text{m}}^{2}}\]

3.            Perimeter of a square piece of gold is 22 millimetres. What is the length of each side of the piece of gold?

(a) 11 millimetres            (b) 5.5 millimetres

(c) 5 millimetres              (d) 4.5 millimetres

(e) None of these

Answer (b) is correct.

Explanation: Here, the perimeter of square piece of gold = 22 millimetres

Since, perimeter = \[4\times \]side of square

Therefore, each side of the square piece of gold \[=\frac{\text{Perimeter}}{4}=\frac{22}{4}\] millimetres = 5.5 millimetres

4.            The figure given below is made up of identical squares. What is the perimeter of the figure?

(a) 54 cm                      (b) 60 cm

(c) 66 cm                      (d) 72 cm

(e) None of these

Answer (b) is correct.

Explanation:

Length of each square = 3 cm

Number of outer sides of all squares = \[2+1+2+1+3+3+1+3+3+1=20\]

Hence, the required perimeter = (\[3\times 20\]) cm = 60 cm

Commonly Asked Question

1. Find the length of GF in the figure given below.

(a) 5 cm                        (b) 6 cm

(c) 7 cm                        (d) 8 cm

(e) None of these

Answer (c) is correct.

Explanation: Here,

BC = AL + KJ + IH + ED + GF = (2 + 1 + 3 + 7) cm + GF = 13 cm + GF = 20 cm

Therefore, GF = BC \[-\] (AL + KJ + IH + ED) = (\[20-13\]) cm = 7 cm

2.            Perimeters of the given rectangle A and square B are same. Find the side of square B.

(a) 5.5 cm                                  (b) 6.0 cm

(c) 6.5 cm                                  (d) 5.0 cm

(e) None of these

Answer (a) is correct.

Explanation: Here, length of rectangle A = 8 cm, and its breadth = 3 cm

Therefore, the perimeter of rectangle A = \[2\times (8+3)\] cm = (\[2\times 11\]) cm = 22 cm

So, we have the perimeter of square B = 22 cm

Since, perimeter of a square = \[4\times \text{side}\]

Hence, the side of square B = \[\frac{\text{Perimeter}}{4}=\frac{22}{4}\] cm = 5.5 cm

3.            Area of triangle BCD is half of the area of rectangle ABCD. Find the area of triangle BCD.

(a) \[25\text{ c}{{\text{m}}^{2}}\]                               

(b) \[26\text{ c}{{\text{m}}^{2}}\]

(c) \[27\text{ c}{{\text{m}}^{2}}\]                               

(d) \[28\text{ c}{{\text{m}}^{2}}\]

(e) None of these

Answer (c) is correct.

Explanation: Here, the length of rectangle ABCD = 18 cm and breadth = 3 cm

Therefore, the area of rectangle ABCD = \[\text{length}\times \text{breadth}=(18\times 3)\text{ c}{{\text{m}}^{2}}=54\text{ c}{{\text{m}}^{2}}\]

Now, the area of triangle BCD = half of the area of rectangle ABCD

Hence, the required area = \[(54\div 2)\text{ c}{{\text{m}}^{2}}=27\text{ c}{{\text{m}}^{2}}\]

4.            Area of inner square PQRS is one-third of the area of outer square ABCD. Find the area of inner square PQRS.

(a) \[27\text{ c}{{\text{m}}^{2}}\]                    

(b) \[\text{18 c}{{\text{m}}^{2}}\]

(c) \[\text{29 c}{{\text{m}}^{2}}\]                               

(d) \[\text{54 c}{{\text{m}}^{2}}\]

(e) None of these

Answer (a) is correct.

Explanation: Here, one side of outer square ABCD = 9 cm

Therefore, the area of outer square ABCD = \[\text{side}\times \text{side}=(9\times 9)\text{ c}{{\text{m}}^{2}}=81\text{ c}{{\text{m}}^{2}}\]

Now, the area of inner square PQRS is one-third of the area of outer square ABCD.

Hence, the required area = \[\frac{81}{3}\text{ c}{{\text{m}}^{2}}=27\text{ c}{{\text{m}}^{2}}\]

5.            In the figure given below, the triangle ABC is an equilateral triangle. Find the perimeter of whole figure.

(a) 30 cm                      (b) 32 cm

(c) 34 cm                      (d) 36 cm

(e) None of these

Answer (d) is correct.

Explanation: Here, \[\text{GH}=\text{FI}-(\text{FG}+\text{HI})=\text{FI}-(\text{BD}+\text{CE})=\left[ \text{12}-(2+2) \right]\text{ cm}\]\[=(12-4)\text{ cm}=8\text{ cm}\]

Since, triangle ABC is an equilateral triangle.

Therefore, AB = AC = BC = GH = 8 cm

Hence, the required perimeter = AB + BD + DF + FI + EI + CE + AC

= (\[8+2+2+12+2+2+8\]) cm = 36 cm