Problems on Area - Solved Examples(Set 2)

Problems on Area - Solved Examples(Set 2)

6. A rectangular field has to be fenced on three sides leaving a side of $20$ feet uncovered. If the area of the field is $680$ sq. feet, how many feet of fencing will be required?
A. $95$	B. $92$
C. $88$	D. $82$

answer with explanation

Answer: Option C
Explanation:
Solution 1

Area of the field $=680$ sq. feet.

Length of the adjacent sides are
$20$ feet and $\frac{680}{20}=34$ feet.

Required length of the fencing
$=20+34+34=88$ feet

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Solution 2

Area of the field $=680$ sq. feet
$\Rightarrow lb=680$ sq. feet

$b=20\text{feet}\Rightarrow l\times 20=680\Rightarrow l=\frac{680}{20}=34\text{feet}$

Required length of the fencing
$=20+(2\times 34)=88$ feet

7. A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is $9$ feet, and the sum of the lengths of the painted sides is $37$ feet, find out the area of the parking space in square feet?
A. $126$ sq. ft.	B. $64$ sq. ft.
C. $100$ sq. ft.	D. $102$ sq. ft.

answer with explanation

Answer: Option A
Explanation:
Solution 1

length $=9$ feet
breadth $=\frac{37-9}{2}=14$ feet

Area $=9\times 14=126$ square feet

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Solution 2

Let $l=9$ feet. Then,

$l+2b=37\Rightarrow 2b=37-l=37-9=28\Rightarrow b=\frac{28}{2}=14\text{feet}$

Area $=lb=9\times 14=126$ square feet

8. The area of a rectangular plot is $460$ square metres. If the length is $15\%$ more than the breadth, what is the breadth of the plot?
A. $14$ metres	B. $20$ metres
C. $18$ metres	D. $12$ metres

answer with explanation

Answer: Option B
Explanation:
Solution 1

$lb=460{\text{m}}^2\cdots \left(1\right)$

Let breadth $=b$
Then length, $l=b\times \frac{(100+15)}{100}=\frac{115b}{100}\cdots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,
$\frac{115b}{100}\times b=460b^2=\frac{46000}{115}=400\Rightarrow b=\sqrt{400}=20\text{m}$

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Solution 2

length $=115\%$ of breadth.

length×breadth $=460{\text{m}}^2$
⇒ $115\%$ of breadth×breadth $=460{\text{m}}^2$
⇒ $\frac{115}{100}\times$ breadth×breadth $=460{\text{m}}^2$
⇒ breadth×breadth $=400{\text{m}}^2$
⇒ breadth $=20\text{m}$

9. 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?
A. $400$	B. $365$
C. $385$	D. $315$

answer with explanation

Answer: Option D
Explanation:
Solution 1

Let area of the larger part $=x$ hectares,
area of the smaller part $=(700-x)$ hectares.

Difference of the areas of the two parts
$=x-(700-x)=2x-700$

one-fifth of the average of the two areas
$=\frac{1}{5}\times \frac{700}{2}=70$(∵ total area is $700$)

Given that difference of the areas of the two parts = one-fifth of the average of the two areas
$\Rightarrow 2x-700=70\Rightarrow 2x=770\Rightarrow x=\frac{770}{2}=385$
Hence, area of smaller part
$=(700-x)=(700–385)=315$ hectares.

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Solution 2

Average of the two areas $=\frac{700}{2}=350$
one-fifth of the average of the two areas$=\frac{350}{5}=70$
⇒ Difference of the two areas $=70$

Let area of the smaller part $=x$ hectares.
Then, area of the larger part $=x+70$ hectares.

$x+(x+70)=700\Rightarrow 2x=630\Rightarrow x=315$

10. The length of a room is $5.5$ m and width is $3.75$ m. What is the cost of paying the floor by slabs at the rate of Rs.$800$ per sq. metre.
A. Rs.$12000$	B. Rs.$19500$
C. Rs.$18000$	D. Rs.$16500$

answer with explanation

Answer: Option D
Explanation:
Area $=5.5\times 3.75$ sq. metre.

Cost for $1$ sq. metre. = Rs.$800$

Hence, total cost
$=5.5\times 3.75\times 800=5.5\times 3000=\text{Rs}.16500$