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# Perimeter Area Volume Questions

## Definition of Perimeter Area Volume • Perimeter is the distance around the closed space of a shape or a closed curve, such as a circle. The formula for calculating perimeters varies on the kind of shape.
• Area can be discussed as the size of space in the interiors of the shape. Area is often measured in square units. Similarly, the formula for calculating area varies on the kind of shape.
• Volume is calculated only for solid 3D shapes, such as cylinder, cubes, spheres and more. The amount of space or mass covered in the object of any shape and size is known as its volume.
• The formulas for 2D and 3D shapes are different as there is np mass or volume of the 2-dimensional shapes.
• Perimeter, area and volume are the measurements of the shapes or geometric figures. Calculating these is a basic concept that is covered in the school level math.
• Most of the competitive examinations gives questions on the same to judge the mental aptitude of the individuals. It is a very easy and scoring topic where students do not have to waste extra time and efforts.
• However, it is important to know all the formulas for different shapes in order to calculate their, area, perimeter and volume.

### Rectangle

• Area = Length * Width
• Perimeter = 2 [Lengths + Widths] ### Triangle

• Area = 1/2 * base * height
• Perimeter = a + b + c (add the length of the three sides)
• Area using Heron’s formula = $S = \frac{a + b + c}{2}$
then, $Area = \sqrt{S(S – a)(S – b)(S – c)}$ ### Cuboid

• Volume = Length * Width * Height
• Surface = 2lw + 2lh + 2wh
• Curved Surface Area = 2h(l + b) ### Cylinder

• Volume = $\pi r^2\times \text{ height }$
• Surface area = $2\pi rh + 2\pi r^2$
• Curved Surface Area = $2\pi rh$ ### Sphere

• Volume = $\frac{4}{3}\pi r^3$
• Surface = $4\pi r^2$ Question 1 Time: 00:00:00
A garden is in the shape of a rectangular field whose sides are in the proportion of 2:3. The garden’s area is 1/6 hectares. What is the breadth of the garden? 150

150

75

75

50

50

25

25

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Question 2 Time: 00:00:00
Find the area of the largest circle which is drawn in a rectangle having sides as 35 cm by 22 cm. 380.28

380.28

219.61

219.61

308.5

308.5

298.41

298.41

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Question 3 Time: 00:00:00
Find the area and perimeter of a rectangular area whose length is 29.5 meters and breadth is 21.8 meters. 612.6 and 94.5

612.6 and 94.5

643.1 and 102.6

643.1 and 102.6

622.8 and 103

622.8 and 103

601.2 and 92.12

601.2 and 92.12

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Question 4 Time: 00:00:00
A rectangular plot is in the ratio 5:4. If Neha is cycling sideways at the boundary of the garden at 12 km/hr speed, she finishes one round of the garden in 12 minutes. Find the area of the garden (in sq. m). 261777

261777

246908.64

246908.64

242022.22

242022.22

262552.05

262552.05

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Question 5 Time: 00:00:00
A room is half as long as it is broad. The cost of flooring it at Rs. 10 per square meter is Rs. 540 and the cost of painting the four walls at Rs. 20 per meter square are Rs. 3440. If the two windows and one door occupies the space of 16-meter square, then find the height of the room. 2

2

5

5

6

6

9

9

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Question 6 Time: 00:00:00
What is the area of the rhombus with one side as 5 cm and one diagonal as 8 meters? 35

35

38

38

32

32

24

24

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Question 7 Time: 00:00:00
A ground is in the shape of a trapezium whose parallel sides are 80 and 50 metres and non-parallel sides are 70 and 48 metres. Find the cost of cultivating the ground at the rate of 95 paisa per square metre? 11400.50

11400.50

15894.28

15894.28

11242.82

11242.82

12509.60

12509.60

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Question 8 Time: 00:00:00
If each side of the rectangle is increased by 42%, then find the increase in the area? 101.64%

101.64%

121.22%

121.22%

152.5%

152.5%

103.6%

103.6%

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Question 9 Time: 00:00:00
The altitude drawn to the base of an isosceles triangle is 10 cm. If the perimeter of the triangle is 40 cm, then find the area. 93.75 cm2

93.75 cm2

90 cm2

90 cm2

89.9cm2

89.9cm2

80cm2

80cm2

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Question 10 Time: 00:00:00
A square field is cultivating at Rs. 117.5 per hectare. The total cost of cultivating it is Rs. 1880. Find the cost of planting around it at the rate of 80 paise per meter. 1600

1600

1280

1280

1950

1950

1900

1900

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Question 11 Time: 00:00:00
A rectangular area is 150 m by 75 m. The area has a boundary of 3 meters wide in the inner part.  Find the area of the boundary and the cost of making it at 78 paise per 1000 cm2. 10650

10650

10358.4

10358.4

10898.3

10898.3

10249.2

10249.2