# Tips And Tricks And Shortcuts on Perimeter Area Volume Questions

## Tips Tricks Shortcuts on Perimeter Area Volume

The area is the space occupied by a shape of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure.And Volume is calculatred by the  quantity of three-dimensional space enclosed by a closed surface. ### Tips And Tricks And Shortcuts on Perimeter Area Volume:-

• Here, are quick and easy tips and tricks for you on Perimeter, Area, and Volume. Learn, the tricks and concept on Perimeter, area and volume.

### Type 1: Find the area, perimeter, length, breadth and some other sides of the shapes

Question 1: The ratio between the length and the breadth of a rectangular plot is 7:3. Rahul was cycling along the boundary of the plot at a speed of 10 km/hr. He completes one round of the plot in 6 minutes. Find the area of the plot?

Options:

A. 52000 m²

B. 51500 m²

C. 53500 m²

D. 52500 m²

Solution:    Distance covered by Rahul in 6 minutes = $\frac{10000}{60}$ × 6 = 1000 m

Therefore, perimeter = 1000m

Length = 7x and breadth = 3x

Then 2 (l +b) = 1000

2 (7x + 3x) = 1000

2 (10x) = 1000

20x = 1000

x = 50

Length = 7x = 7 * 50 = 350

Breadth = 3x = 3 * 50 = 150

Therefore, Area = l * b = 350 * 150 = 52500 m²

Correct option: D

### Type 2: Perimeter, Area and Volume Tips and Tricks and Shortcuts by finding the volume & surface area

Question 1 What is the total surface area of a right circular cone of height 10 cm and base radius 7 cm?

Options:

A. 422.4 m²

B. 422.4 cm²

C. 422.4 cm³

D. 422.4 cm

Solution:    h = 10 cm, r = 7 cm

Slant height = l = $\sqrt{h^2 + r^2 }$

l = $\sqrt{100 + 49 }$ = $\sqrt{149 }$= 12.2

Total surface area of cone = πrl + πr²

($\frac{22}{7}$ × 7 × 12.2 )+ ($\frac{22}{7}$ × 7 ×  7 )

268.4 + 154

422.4 cm²

Correct option: B

### Type 3:Tips and Tricks and Shortcuts for Perimeter, Area and Volume by finding Percentage increase or decrease

Question 1:If length of the rectangle is increased by 50% and breadth is decreased by 20%. Then what is the percentage change in the area?

Options:

A. 70% decrease

B. 30 % increase

C. 20% increase

D. 20% decrease

Solution:     Original area = l * b

New length = 50% increase = $\frac{150}{100}$l

= $\frac{3}{2}$l
New breadth = 20% decrease = $\frac{80}{100}$b = $\frac{4}{5}$b

Therefore, new area = $\frac{3}{2}$l  * $\frac{4}{5}$b

New area =$\frac{6}{5}$ l b

Change in Area = New Area – Original Area

Change in Area = $\frac{6}{5}$lb – lb

Change in Area = $\frac{1}{5}$lb

Percentage change in area = $\frac{\frac{1}{5}lb}{lb}$ * 100

Percentage change in area = $\frac{1}{5}$ * 100 = $\frac{100}{5}$ = 20%

Since, the answer is positive, it means there is increase in the area.

Correct option: C

### Type 4: How to solve cost related problems

Question 1 A wall of trapezium shape has height 8 m. The parallel sides of trapezium are 4 m and 6 m. If the rate of painting per square meter is Rs.50 than find the cost painting the complete wall?

Options:

A. Rs. 400

B. Rs. 420

C. Rs. 540

D. Rs. 450

Solution:    Area of trapezium =$\frac{1}{2}$ * (sum of parallel sides) * distance between them

Area of trapezium = $\frac{1}{2}$ * (4 + 6) + 8

Area of trapezium = $\frac{1}{2}$ * (18)

Area of trapezium = 9 square meter

Rate of painting per square meter is Rs.50

Therefore, to paint 9 square meter, total cost of painting = 9 * 50 = Rs. 450