# Area

The length of a rectangular hall is 5 m more than its breadth. The area of the hall is 750 m. The length of the hall is

Then, length = (x + 5) m

x(x + 5) = 750

x² + 5x - 750= 0

⇒ (x + 30) (x-25)= 0

x = 25

The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 7500 sq. m, the cost of fencing the field @ 25 paise per metre is :

Let length = (3x) metres and breadth = (4x) metres.

Then, 3x × 4x = 7500

⇒ 12x2 = 7500
⇒ x2 = 625
⇒ x = 25.

So, length = 75 m and breadth = 100 m.

Perimeter = [2(75 + 100)] m
= 350 m.

∴ Cost of fencing = Rs. (0.25 × 350)
= Rs. 87.50.

A rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :

Required perimeter = (AB + BC  + CP + PQ + QR + RA)

= AB + BC + (CP + QR) + (PQ + RA)

= AB + BC + AB + BC

= 2 (AB + BC)

= [2 (8 + 4 )] cm

= 24 cm.

A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares ?

Let the areas of the two parts be x and (700 − x) hectares respectively. Then,

[x - (700 - x)] = $$\frac{1}{5} \times \left [ \frac{x + \left ( 700 - x \right )}{2} \right ]$$

⇒ 2x - 700  = 70

⇒ x = 385.

So, area of smaller part

= (700 - 385) hectares

= 315 hectares.

A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?

When folded along breadth, we have,
$$2 \left ( \frac{l}{2} + b \right ) = 34$$ or l + 2b = 34 .... (i)

When folded along length, we have,
$$2 \left ( l + \frac{b}{2} \right ) = 38$$ or 2l + b = 38 .... (ii)

Solving (i) and (ii), we get : l = 14 and b = 10.

∴ Area of the paper = (14 × 10) cm2 = 140 cm2.

The length of a rectangular hall is 5 m more than its breadth. The area of the hall is 7502. The length of the hall is :

Then, length = (x + 5) metres.

Then, x(x + 5) = 750

⇒ x2 + 5x - 750 = 0

⇒ (x + 30) (x - 25) = 0

x = 25.

∴ Length = (x + 5) = 30 m.

It is decided to construct a 2 metre broad pathway around a rectangular plot on the inside. If the area of the plots is 96 sq.m. and the rate of construction is Rs. 50 per square metre., what will be the total cost of the construction?

Let length and width of the rectangular plot be l and b respectively

Total area of the rectangular plot = 96 sq.m.
⇒ lb = 96

Width of the pathway = 2 m

Length of the remaining area in the plot = (l - 4)

breadth of the remaining area in the plot = (b - 4)

Area of the remaining area in the plot = (l - 4) (b - 4)

Area of the pathway
= Total area of the rectangular plot - remaining area in the plot

= 96 - [(l - 4)(b - 4)]
= 96 - [lb - 4l - 4b + 16]
= 96 - [96 - 4l - 4b + 16]
= 96 - 96 + 4l + 4b - 16
= 4l + 4b - 16
= 4(l + b) - 16

We do not know the values of l and b and hence area of the pathway cannot be found out. So we cannot determine total cost of the construction.

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

Question seems to be typical,but trust me it is too easy to solve,before solving this, lets analyse how we can solve this.

We are having speed and time so we can calculate the distance or perimeter in this question.

Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Let's solve it:

Perimeter = Distance travelled in 8 minutes,

⇒ Perimeter = 12000/60 × 8
= 1600 meter.   [because Distance = Speed × Time]

As per question length is 3x and width is 2x We know perimeter of rectangle is,

2 ( L + B) So, 2(3x + 2x) = 1600
⇒ x = 160

So Length = 160 × 3 = 480 meter
and Width = 160 × 2 = 320 meter

Finally, Area = length × breadth
= 480 × 320
= 153600

A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is.

Weight = $$\frac{18}{25} \times 50$$
Number = $$\frac{800 \times 700 \times 600}{8} \times 7 \times 6$$