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Perimeter and Area of Rectangles, Triangles, Circles

by VISHNUPRIYA
(AHMEDABAD)

Perimeter and Area

1. Find the perimeter and area of a rectangle of length 16 cm and breadth 12.5 cm.
a.rectangle | height 16 cm (centimetres) | area
Width 12.50 cm (centimetres) | perimeter
Area | 200 cm^2 (square centimetres)
Perimeter | 57 cm (centimetres)
2. The perimeter of a rectangular field is 216 metres and its breadth is 40 metres.Find the length and area of the rectangle.
3. The perimeter of a rectangle is equal to that of a square with side 13m. If the rectangle is 16m long, what is its breadth?
4. A wire is in the shape of a square of side 15cm.If the wire is rebent into a rectangle of length 18cm, find its breadth. Which encloses more area, the square or the rectangle?
5.The dimensions of a room are 11.2m by 9m. The floor of the room is to be covered by marble tiles, each measuring 24cm by 24cm.Find the total number of tiles required. What is the cost of tiling the floor at Rs 6 per tile?
6. Find the area of a triangle, whose base is 9.6cm, and the corresponding altitude is 5cm.
7. Find the altitude of a triangle whose area is 45 sq. cm and base is 15cm.
8. The adjacent sides of a parallelogram are 36cm and 27cm in length. If the perpendicular distance between the shorter sides is 12cm, find the distance between the longer sides.
9.The area of a parallelogram with height 7.5cm is 71.25 sq cm.what is the corresponding base of a parallelogram?
10.Find the area of an isosceles right triangle if one of the right sides is 20cm long.
11. Find the area of right triangle whose two sides containing the right angle measure 3cm and 4cm.
12. Find the area of circle whose diameter is 7cm.
13. The circumference of a circle is 440 metres.Find its diameter and area.
14. The diameter of a circular field is 98m.If a child walks at the rate of 14m per minute, how long will it take for her to walk round the field?
15. From a rectangular piece of metal sheet of length and breadth 1.6m and 80cm respectively, three circular sheets of 20cm radius are cut out. What area of metal is left?
16. The inner and outer radii of a cylindrical pipe are 5cm and 4cm respectively, find the area of cross-section of the pipe. (π=3.14)
17. A room is 10m long and 6cm broad .It is surrounded by a veranda which is 2m wide all around it.Find the cost of flooring the veranda with marble at Rs36 per sq m.
18.Two cross roads,each of width 2m,run at right angles through the centre of a rectangular park of length 76m and breadth 54m and parallel to its sides.Find the area of the roads. Also find the cost of constructing the roads at the rate of Rs16 per sq m.

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Jan 22, 2013

Perimeter and Area
by: Staff

Answer

Part I

1. Find the perimeter and area of a rectangle of length 16 cm and breadth 12.5 cm.

P_rectangle = 2L_rectangle + 2W_rectangle

= 2*16 + 2*12.5

= 57

P_rectangle = 57 cm

A_rectangle = LW

= 16*12.5

= 200

A_rectangle = 200 cm²

2. The perimeter of a rectangular field is 216 metres and its breadth is 40 metres. Find the length and area of the rectangle.

P_field = 2L_field + 2W_field

216 = 2*L_field + 2*40

2*L_field + 2*40 = 216

2*L_field + 80 = 216

2*L_field + 80 - 80 = 216 - 80

2*L_field + 0 = 136

2*L_field = 136

2*L_field / 2 = 136 / 2

L_field = 136 / 2

L_field = 68 metres

L_field = 68 metres

A_field = L_fieldW_field

= 68*40

= 2720 m²

A_field = 2720 m²

3. The perimeter of a rectangle is equal to that of a square with side 13m. If the rectangle is 16m long, what is its breadth?

P_rectangle = 2L_rectangle + 2W_rectangle

P_square = 4S_square

P_square = 4*13 = 52 m

P_rectangle = 2L_rectangle + 2W_rectangle

52 m = 2L_rectangle + 2W_rectangle

52 m = 2*16 + 2W_rectangle

2*16 + 2W_rectangle = 52

32 + 2W_rectangle = 52

32 - 32 + 2W_rectangle = 52 - 32

0 + 2W_rectangle = 20

2W_rectangle = 20

2W_rectangle / 2 = 20 / 2

W_rectangle = 20 / 2

W_rectangle = 10 m

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Jan 22, 2013

Perimeter and Area
by: Staff

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Part II

4. A wire is in the shape of a square of side 15 cm. If the wire is rebent into a rectangle of length 18 cm, find its breadth. Which encloses more area, the square or the rectangle?

P_{wire square} = 4S_{wire square}

P_{wire square} = 4*15 = 60 cm

P_{wire rectangle} = 2L_{wire rectangle} + 2W_{wire rectangle}

60 cm = 2L_{wire rectangle} + 2W_{wire rectangle}

60 cm = 2*18 + 2W_{wire rectangle}

2*18 + 2W_{wire rectangle} = 60

36 + 2W_{wire rectangle} = 60

36 - 36 + 2W_{wire rectangle} = 60 - 36

0 + 2W_{wire rectangle} = 24

2W_{wire rectangle} = 24

2W_{wire rectangle} / 2 = 24 / 2

W_{wire rectangle} = 24 / 2

W_{wire rectangle} = 12

W_{wire rectangle} = 12 cm

A_{wire square} = S²_{wire square}

= 15²

= 225 cm²

A_{wire rectangle} = L_{wire rectangle}W_{wire rectangle}

= 18*12

= 216 cm²

A_{wire square} > A_{wire rectangle}; 225 cm² > 216 cm²

5.The dimensions of a room are 11.2 m by 9 m. The floor of the room is to be covered by marble tiles, each measuring 24 cm by 24 cm. Find the total number of tiles required. What is the cost of tiling the floor at Rs 6 per tile?

A_room = L_roomW_room

= 11.2*9

= 100.8 m²

1 m² = 10,000 cm²

A_{room in cm²} = (100.8 m²) * (10,000 cm² / m²)

= 100.8 * 10000

= 1,008,000 cm²

A_{single tile in cm²} = (24 cm) * (24 cm)

= 24 * 24

= 576 cm²

Number of Tiles Required = (A_{room in cm²}) / (A_{single tile in cm²})

Number of Tiles Required = (1,008,000 cm²) / (576 cm²)

= 1750

Number of Tiles Required = 1750

Cost = (Number of Tiles Required) * (Rs 6 per tile)

= 1750 * 6

= 10500

Cost = Rs 10500

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Jan 22, 2013

Perimeter and Area
by: Staff

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Part III

6. Find the area of a triangle, whose base is 9.6 cm, and the corresponding altitude is 5 cm.

A_triangle = ½*b_triangleh_triangle

= ½*9.6*5

= 24

A_triangle = 24 cm²

7. Find the altitude of a triangle whose area is 45 sq. cm and base is 15 cm.

A_triangle = ½*b_triangleh_triangle

45 = ½ * 15 * h_triangle

½ * 15 * h_triangle = 45

7.5 * h_triangle = 45

7.5 * h_triangle / 7.5 = 45 / 7.5

h_triangle = 45 / 7.5

h_triangle = 6

h_triangle = 6 cm

8. The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the perpendicular distance between the shorter sides is 12 cm, find the distance between the longer sides.

A_{parallelogram} = b_{short side}h_{between short sides}

= 27*12

= 324 cm²

A_{parallelogram} = b_{long side}h_{between long sides}

324 = 36 * h_{between long sides}

36 * h_{between long sides} = 324

36 * h_{between long sides} / 36 = 324 / 36

h_{between long sides} = 324 / 36

h_{between long sides} = 9

h_{between long sides} = 9 cm

9. The area of a parallelogram with height 7.5 cm is 71.25 sq cm. What is the corresponding base of a parallelogram?

A_{parallelogram} = b_{parallelogram}h_{parallelogram}

71.25 = b_{parallelogram} * 7.5

b_{parallelogram} * 7.5 = 71.25

b_{parallelogram} * 7.5 / 7.5 = 71.25 / 7.5

b_{parallelogram} = 71.25 / 7.5

b_{parallelogram} = 9.5

b_{parallelogram} = 9.5 cm

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Jan 22, 2013

Perimeter and Area
by: Staff

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Part IV

10. Find the area of an isosceles right triangle if one of the right sides is 20 cm long.

b_{isosceles right triangle} = h_{isosceles right triangle} = 20 cm

A_{isosceles right triangle} = ½*b_{isosceles right triangle}h_{isosceles right triangle}

A_{isosceles right triangle} = ½ * 20 * 20

A_{isosceles right triangle} = 200

A_{isosceles right triangle} = 200 cm²

11. Find the area of right triangle whose two sides containing the right angle measure 3 cm and 4 cm.

A_{right triangle} = ½*b_{right triangle}h_{right triangle}

A_{right triangle} = ½ * 3 * 4

A_{right triangle} = 6

A_{right triangle} = 6 cm²

12. Find the area of circle whose diameter is 7 cm.

r_circle = d_circle / 2

r_circle = 7 / 2

r_circle = 3.5

A_circle = π*r²_circle

= π * 3.5²

= π * 12.25

= 38.484510006475

A_circle = 38.5 cm²

13. The circumference of a circle is 440 metres. Find its diameter and area.

C_circle = π*d_circle

440 = π*d_circle

π*d_circle = 440

π*d_circle / π = 440 / π

d_circle = 440 / π

d_circle = 140.0563499208679

d_circle = 140.1 m

A_circle = π*r²_circle

A_circle = π*(d_circle/2)²

= π * (140.0563499208679/2)²

= π * 4903.9452882891483

= 15406.198491295469

A_circle = 15406.2 m²

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Jan 22, 2013

Perimeter and Area
by: Staff

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Part V

14. The diameter of a circular field is 98 m. If a child walks at the rate of 14 m per minute, how long will it take for her to walk around the field?

C_circle = π*d_circle

= π*98

= 307.8760800517997 m is the distance around the field

d_{around circle} = r_{rate child walks} * t_minutes

307.8760800517997 m = (14 m / min) * t_minutes

(14) * t_minutes = 307.8760800517997

(14) * t_minutes / 14 = 307.8760800517997 / 14

t_minutes = 307.8760800517997 / 14

t_minutes = 21.9911485751285

t_minutes = 22.0 minutes

15. From a rectangular piece of metal sheet of length and breadth 1.6 m and 80 cm respectively, three circular sheets of 20 cm radius are cut out. What area of metal is left?

A_{metal left} = A_{entire metal sheet} - A_{circular sheets}

A_{metal left} = A_{entire metal sheet} - 3*A_{one circular sheet}

1 m = 100 cm

L_{entire metal sheet in cm} = L_{entire metal sheet in m} * 100

L_{entire metal sheet in cm} = 1.6 * 100

L_{entire metal sheet in cm} = 160 cm

A_{entire metal sheet} = L_{entire metal sheet}W_{entire metal sheet}

= 160 * 80

= 12800 cm²

A_{one circular sheet} = π*r²_{one circular sheet}

= π * (20)²

= π * 400

= 1256.6370614359173 cm²

A_{metal left} = A_{entire metal sheet} - 3*A_{one circular sheet}

= 12800 - 3*1256.6

= 12800 - 3769.8

= 9030.2

A_{metal left} = 9030.2 cm²

16. The inner and outer radii of a cylindrical pipe are 5 cm and 4 cm respectively, find the area of cross-section of the pipe. (π=3.14)

A_{cross-section of the pipe} = A_{cross-section to outer radius} - A_{cross-section to inner radius}

A_{cross-section of the pipe} = π*r²_{outer radius} - π*r²_{inner radius}

A_{cross-section of the pipe} = 3.14*r²_{outer radius} - 3.14*r²_{inner radius}

= 3.14*5² - 3.14*4²

= 3.14*25 - 3.14*16

= 78.50 - 50.24

= 28.26 cm²

A_{cross-section of the pipe} = 28.26 cm²

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Jan 22, 2013

Perimeter and Area
by: Staff

------------------------------------------------------

Part VI

17. A room is 10 m long and 6 cm broad . It is surrounded by a veranda which is 2 m wide all around it. Find the cost of flooring the veranda with marble at Rs36 per sq m.

6 cm broad ? I’m going to assume you really mean 6 m broad

A_veranda = A_{room + veranda} - A_{room only}

A_{room + veranda} = L_{room + veranda}W_{room + veranda}

L_{room + veranda} = 10 + 2 + 2

= 14

W_{room + veranda} = 6 + 2 + 2

= 10 m

A_{room + veranda} = 14*10

= 140 m²

A_{room only} = L_{room only}W_{room only}

L_{room only} = 10 m

W_{room only = 6 m

A_{room only} = 10*6

= 60 m²

A_veranda = A_{room + veranda} - A_{room only}

= 140 m² - 60 m²

= 80 m²

C_{veranda flooring} = A_veranda * (cost per m²)

= 80 * (Rs 36)

= Rs 2880

Cost_{veranda flooring} = Rs 2880}

18. Two cross roads, each of width 2 m, run at right angles through the centre of a rectangular park of length 76 m and breadth 54 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of Rs16 per sq m.

A_roads = A_road-1 + A_road-2 - A_{adjustment for double counting}

= 76*2 + 54*2 - 2*2

= 152 + 108 - 4

= 256

A_roads = 256 m²

C_{cost of construction} = A_roads * (cost per m²)

= 256 * (Rs 16)

= Rs 4096

C_{cost of construction} = Rs 4096

Thanks for writing.

Staff
www.solving-math-problems.com

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Perimeter and Area of Rectangles, Triangles, Circles

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