Cost Estimation Based on Perimeter for Fencing Problems
Cost Estimation Based on Perimeter calculates the total expense for fencing, wiring, painting borders or constructing walls around a figure. The basic rule is to multiply the complete perimeter by the cost per unit length. Correct unit conversion, number of rounds and the given rate determine the final answer.
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What Is Cost Estimation Based on Perimeter?
Use the formula Total cost = Perimeter × Rate per unit length. If the work is done in multiple rounds, multiply the perimeter by the number of rounds first. For a rectangle of length 18 m and breadth 10 m, the perimeter is 2(18 + 10) = 56 m. At ₹25 per metre, the cost is 56 × 25 = ₹1,400.
Cost Estimation Based on Perimeter Video Lessons
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Cost Estimation in Mensuration
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Cost Estimation Based on Perimeter Formula & Tricks
Important Formulas
Use this when the boundary is covered once and the rate is given per metre or other unit length.
Here, l is the length and b is the breadth of the rectangle.
Here, a is the side of the square.
Here, P is the perimeter, n is the number of rounds and R is the rate per unit length.
These rearranged formulas find the rate or perimeter when the other two values are known.
Quick Tricks
Do not multiply the rate by area or by the sum of only two sides. Calculate the complete perimeter before finding cost.
For n rounds, the required length is n times the perimeter. The cost also becomes n times the one-round cost.
The perimeter unit must match the rate unit. Convert centimetres to metres when the rate is given per metre.
If two boundaries have equal perimeters and the same rate, their costs are equal, even when their shapes differ.
Cost Estimation Based on Perimeter Concepts
Single-round fencing or boundary work
First calculate the perimeter of the given shape. Then multiply it by the rate. For a rectangle with l = 20 m and b = 7 m, P = 2(20 + 7) = 54 m. At ₹30 per metre, total cost = 54 × 30 = ₹1,620.
Cost for multiple rounds
The total fencing length is P × n, where n is the number of rounds. For a square with side 14 m, P = 4 × 14 = 56 m. Three rounds require 56 × 3 = 168 m; at ₹18 per metre, the cost is ₹3,024.
Using the rectangle and square formulas
A rectangle has two equal lengths and two equal breadths, while all four sides of a square are equal. For a square of side 16 m, P = 4 × 16 = 64 m. At ₹22 per metre, the cost is 64 × 22 = ₹1,408.
Unit conversion in perimeter cost problems
Since 1 m = 100 cm and 1 km = 1,000 m, a rate of ₹12 per metre cannot be directly multiplied by a perimeter in centimetres. For a boundary of 2,400 cm, convert it to 24 m; the cost at ₹12 per metre is ₹288.
Cost Estimation Based on Perimeter Visual Guide
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Rectangular boundary used for cost calculation
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Cost Estimation Based on Perimeter: Revision Points
Recall these formulas and calculation rules for perimeter-based cost problems.
- Total cost = Perimeter × Rate per unit length.
- Rectangle perimeter = 2(l + b).
- Square perimeter = 4a.
- For n rounds, total cost = P × n × rate.
- Match the perimeter unit with the rate unit before multiplication.
- At the same rate, equal perimeters produce equal costs.
- Area is not used when the charge is based on boundary length.
Cost Estimation Based on Perimeter FAQs
What is the cost estimation based on perimeter formula?
Total cost = Perimeter × Rate per unit length. For multiple rounds, use Total cost = Perimeter × Number of rounds × Rate.
What is the cost of fencing a 25 m by 15 m rectangle at ₹40 per metre?
Its perimeter is 2(25 + 15) = 80 m. The cost is 80 × 40 = ₹3,200.
How is cost calculated for two rounds around a square of side 9 m at ₹25 per metre?
The square perimeter is 4 × 9 = 36 m. Two rounds require 72 m, so the cost is 72 × 25 = ₹1,800.
What should be done when the perimeter is given in centimetres and the rate is per metre?
Convert the perimeter to metres by dividing by 100. For example, 650 cm = 6.5 m before applying a per-metre rate.
What is the rate per metre if fencing a 60 m perimeter costs ₹2,400?
Rate = Total cost ÷ Perimeter = 2,400 ÷ 60 = ₹40 per metre.
Does area affect a cost charged on perimeter?
No. When the rate is based on boundary length, only the perimeter, number of rounds and rate determine the cost. Area is not required.