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A PROJECT REPORT on Finding the Cost to Construct a Path Submitted to: Yam Pandeya Sindhu Subha Prabhat English Boarding School Kamalamai – 4, Dhurabazar, Sindhuli Submitted by: Aliza Blon Class: IX Roll No: 1 In Partial Fulfillment of Second Terminal Examination of Optional Mathematics Phalgun, 2077

Acknowledgment At first, I would like to express my special thanks of gratitude to my subject teacher Mr. Yam Pandeya who gave me the golden opportunity to do this wonderful project work on the topic \"Finding the cost to Construct a Path\" which taught me so many new things. Secondly, I would also like to thank my school principal Mr. Bhimsen Thapa and all the teaching and non-teach staff of this school who helped me a lot in finalizing this project within the limited time frame, despite their busy schedules. Similarly, I would like to thank my friends who helped me a lot in gathering different information, collecting data, and guiding me from time to time in making this project they gave me different ideas in making this project unique. Thank you, Aliza Blown Class- IX EVALUATION AND APPROVAL This project report has been evaluated and approved. …….……………… ………….……………… Mr. Yam Pandeya Mr. Bhimsen Thapa Subject Teacher Principal Table of content i

Acknowledgment i Evaluation and approval Introduction ii Objectives of project 1 Materials used 1 Procedure 1 Area of garden 1 Area of path 1 Number of tiles 2 Total cost 3 Finding 4 Conclusion 4 5 ii

Introduction The works related to the construction of footpaths around gardens, playgrounds, and swimming pools come into our daily life. These types of problems have been included in the compulsory mathematics curriculum of class nine to make the students able to solve these problems. To make the learning practical and sustainable we are going to conduct project work. Under this project, we going find the area of 1.5m wide path around our school ground and find the total cost to pave bricks on this path. Objective of Project The main objectives of this projects were as follows: i) Calculate the area of the playground of our school. ii) To find the area of 1.5m width path around the garden. iii) To find the total cost to pave tiles on the garden. Materials used measuring tape, pencil, scale, color pencil, scale Procedure This project follows the following procedure: i) Find the length and breadth of the playground of our school. l= 37.10m B A b= 10.30m C1 D

ABCD is a playground of our school, whose length AB = CD = 37.10m and breadth AD = BC = 10.30m. This is a rectangular garden thus the Area of this garden = 37.10m×10.30m = 382.13m2. ii) Find the area of a 1.5m wide path around the garden. A l= 37.10m B E 1.5m F l = 10.30m H G D C Here we are going to construct a 1.5m wide path inside the garden. ABCD is the garden with a path and EFGH is the ground without a path. Now, length of garden AB = CD = 37.10m length of ground without path EF = GH = 37.10m - 2×1.5m = 37.10m – 3m = 34.10m Similarly, Breadth of the ground AD = BC = 10.30m Breadth of ground without path is EH = FG = 10.30m - 2×1.5m = 10. 30m – 3m = 7.30m 2

Area of EFGH = 34.10m×7.30m = 248.93m2 Area of the path = Area of ABCD – Area of EFGH = 382.13m2 - 248.93m2 = 133.19m2 iii) Find the area of each tiles. Under this project, we are going to find the total cost to pave the tiles on the path. Well, there is usually rectangular, square, and pentagonal shape of tiles found in Nepal. The square tiles of size 6\"×6\", 8\"×8\", 12\"×12\" are found in the market of Nepal. But in the market Sindhuli district 8\"×8\" or 20.32cm×20.32cm size tiles were mostly used. Pentagonal shape tiles Square shape tiles Area of each tile = 20.32cm ×20.32cm 3 = 0.2032m×0.2032m = 0.04129024m2

iv) Find number of tiles used to pave the path. Area of path = area of all tiles Area of path= number of tiles × area of each tile Area of path ∴ Number of tiles = Area of each tile 133.19m2 = 0.04129024m2 = 3226 v) Find the total cost to pave tiles on the path. The main objective of the project was to find the total cost of paving tiles on the path. For that first, we find the rate of tile. In the market of the rate of tile is Rs.51.50. Thus, Total cost = Rate of tile × Numbers of tiles = Rs51.50×3226 = Rs. 1,66,123 Finding: Suppose the length of the field of ground be l and its breadth of the ground be b. If we denote the width of the path by d then the length of ground without the path will be l – 2d and the breadth of the ground will be b-2w. Area of path = Area of ABCD – Area of EFGH = l × b - (l - 2d)(b – 2d) = lb – lb + 2ld + 2bd - 4d2 4

= 2ld + 2bd – 4d2 = 2d(l + b – 2d Conclusion: The area of path of 'd' unit with inside the ground of length 'l' and breadth 'b' con be found by using formula Area of path(A) = 2d(l + b – 2d). The number of tiles can be found by dividing area of path by the area of each tiles and the total cost of paving tiles can be found by dividing the price per tile by the number of the tiles. Thus, if we denote area of path by 'A', area of each path by 'a' and rate by 'R' then, A Number of tiles(N) = a and Cost(C) = R×N Thank you 5