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Perimeter and Area of Rectangles, Triangles, Circles
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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.


Prectangle = 2Lrectangle + 2Wrectangle

= 2*16 + 2*12.5

= 57

Prectangle = 57 cm


Arectangle = LW

= 16*12.5

= 200

Arectangle = 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.


Pfield = 2Lfield + 2Wfield

216 = 2*Lfield + 2*40

2*Lfield + 2*40 = 216

2*Lfield + 80 = 216

2*Lfield + 80 - 80 = 216 - 80

2*Lfield + 0 = 136

2*Lfield = 136

2*Lfield / 2 = 136 / 2

Lfield = 136 / 2

Lfield = 68 metres

Lfield = 68 metres


Afield = LfieldWfield

= 68*40

= 2720 m²

Afield = 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?


Prectangle = 2Lrectangle + 2Wrectangle

Psquare = 4Ssquare

Psquare = 4*13 = 52 m

Prectangle = 2Lrectangle + 2Wrectangle

52 m = 2Lrectangle + 2Wrectangle

52 m = 2*16 + 2Wrectangle

2*16 + 2Wrectangle = 52

32 + 2Wrectangle = 52

32 - 32 + 2Wrectangle = 52 - 32

0 + 2Wrectangle = 20

2Wrectangle = 20

2Wrectangle / 2 = 20 / 2

Wrectangle = 20 / 2

Wrectangle = 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?

Pwire square = 4Swire square

Pwire square = 4*15 = 60 cm

Pwire rectangle = 2Lwire rectangle + 2Wwire rectangle

60 cm = 2Lwire rectangle + 2Wwire rectangle

60 cm = 2*18 + 2Wwire rectangle

2*18 + 2Wwire rectangle = 60

36 + 2Wwire rectangle = 60

36 - 36 + 2Wwire rectangle = 60 - 36

0 + 2Wwire rectangle = 24

2Wwire rectangle = 24

2Wwire rectangle / 2 = 24 / 2

Wwire rectangle = 24 / 2

Wwire rectangle = 12

Wwire rectangle = 12 cm

Awire square = S²wire square

= 15²

= 225 cm²


Awire rectangle = Lwire rectangle Wwire rectangle

= 18*12

= 216 cm²

Awire square > Awire 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?


Aroom = LroomWroom

= 11.2*9

= 100.8 m²

1 m² = 10,000 cm²

Aroom in cm² = (100.8 m²) * (10,000 cm² / m²)

= 100.8 * 10000

= 1,008,000 cm²

Asingle tile in cm² = (24 cm) * (24 cm)

= 24 * 24

= 576 cm²

Number of Tiles Required = (Aroom in cm²) / (Asingle 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.


Atriangle = ½*btrianglehtriangle

= ½*9.6*5

= 24

Atriangle = 24 cm²




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


Atriangle = ½*btrianglehtriangle

45 = ½ * 15 * htriangle

½ * 15 * htriangle = 45

7.5 * htriangle = 45

7.5 * htriangle / 7.5 = 45 / 7.5

htriangle = 45 / 7.5

htriangle = 6

htriangle = 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.

Aparallelogram = bshort sidehbetween short sides

= 27*12

= 324 cm²

Aparallelogram = blong sidehbetween long sides

324 = 36 * hbetween long sides

36 * hbetween long sides = 324

36 * hbetween long sides / 36 = 324 / 36

hbetween long sides = 324 / 36

hbetween long sides = 9

hbetween 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?


Aparallelogram = bparallelogramhparallelogram

71.25 = bparallelogram * 7.5

bparallelogram * 7.5 = 71.25

bparallelogram * 7.5 / 7.5 = 71.25 / 7.5

bparallelogram = 71.25 / 7.5

bparallelogram = 9.5

bparallelogram = 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.


bisosceles right triangle = hisosceles right triangle = 20 cm

Aisosceles right triangle = ½*bisosceles right trianglehisosceles right triangle

Aisosceles right triangle = ½ * 20 * 20

Aisosceles right triangle = 200


Aisosceles right triangle = 200 cm²



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


Aright triangle = ½*bright trianglehright triangle

Aright triangle = ½ * 3 * 4

Aright triangle = 6


Aright triangle = 6 cm²




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


rcircle = dcircle / 2

rcircle = 7 / 2

rcircle = 3.5


Acircle = π*r²circle

= π * 3.5²

= π * 12.25

= 38.484510006475


Acircle = 38.5 cm²



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


Ccircle = π*dcircle

440 = π*dcircle

π*dcircle = 440

π*dcircle / π = 440 / π

dcircle = 440 / π

dcircle = 140.0563499208679

dcircle = 140.1 m


Acircle = π*r²circle

Acircle = π*(dcircle/2)²

= π * (140.0563499208679/2)²

= π * 4903.9452882891483

= 15406.198491295469


Acircle = 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?


Ccircle = π*dcircle

= π*98

= 307.8760800517997 m is the distance around the field

daround circle = rrate child walks * tminutes

307.8760800517997 m = (14 m / min) * tminutes

(14) * tminutes = 307.8760800517997

(14) * tminutes / 14 = 307.8760800517997 / 14

tminutes = 307.8760800517997 / 14

tminutes = 21.9911485751285

tminutes = 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?


Ametal left = Aentire metal sheet - Acircular sheets

Ametal left = Aentire metal sheet - 3*Aone circular sheet

1 m = 100 cm

Lentire metal sheet in cm = Lentire metal sheet in m * 100

Lentire metal sheet in cm = 1.6 * 100

Lentire metal sheet in cm = 160 cm

Aentire metal sheet = Lentire metal sheetWentire metal sheet

= 160 * 80

= 12800 cm²

Aone circular sheet = π*r²one circular sheet

= π * (20)²

= π * 400

= 1256.6370614359173 cm²

Ametal left = Aentire metal sheet - 3*Aone circular sheet

= 12800 - 3*1256.6

= 12800 - 3769.8


= 9030.2

Ametal 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)


Across-section of the pipe = Across-section to outer radius - A cross-section to inner radius

Across-section of the pipe = π*r²outer radius - π*r²inner radius

Across-section of the pipe = 3.14*r²outer radius - 3.14*r²inner radius

= 3.14*5² - 3.14*4²

= 3.14*25 - 3.14*16

= 78.50 - 50.24

= 28.26 cm²

Across-section of the pipe = 28.26 cm²




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Jan 22, 2013
Perimeter and Area
by: Staff


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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

Averanda = Aroom + veranda - Aroom only

Aroom + veranda = Lroom + verandaWroom + veranda

Lroom + veranda = 10 + 2 + 2

= 14

Wroom + veranda = 6 + 2 + 2

= 10 m

Aroom + veranda = 14*10

= 140 m²


Aroom only = Lroom onlyWroom only

Lroom only = 10 m

Wroom only = 6 m

Aroom only = 10*6

= 60 m²


Averanda = Aroom + veranda - Aroom only

= 140 m² - 60 m²

= 80 m²


Cveranda flooring = Averanda * (cost per m²)

= 80 * (Rs 36)

= Rs 2880

Costveranda 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.


Aroads = Aroad-1 + Aroad-2 - Aadjustment for double counting

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

= 152 + 108 - 4

= 256

Aroads = 256 m²

Ccost of construction = Aroads * (cost per m²)

= 256 * (Rs 16)

= Rs 4096

Ccost of construction = Rs 4096







Thanks for writing.

Staff
www.solving-math-problems.com



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