# Perimeter and Area of Rectangles, Triangles, Circles

by VISHNUPRIYA

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.

### Comments for Perimeter and Area of Rectangles, Triangles, Circles

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

 Jan 22, 2013 Perimeter and Area by: Staff ------------------------------------------------------ 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 ------------------------------------------------------

 Jan 22, 2013 Perimeter and Area by: Staff ------------------------------------------------------ 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 ------------------------------------------------------

 Jan 22, 2013 Perimeter and Area by: Staff ------------------------------------------------------ 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 ------------------------------------------------------

 Jan 22, 2013 Perimeter and Area by: Staff ------------------------------------------------------ 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 ------------------------------------------------------