Math Problem Statement

The diagram shows a plot of land in the shape of a square PQRS owned by Susan. Susan plants vegetables in the coloured region. She fenced the region at a cost of RM40 per meter. Find the amount of money that must be paid by Susan to fence the region.

Solution

The problem shows a square plot of land PQRSPQRS with a small rectangular region fenced off for planting. The fencing cost is RM 40 per meter, and the goal is to calculate the total cost of fencing the colored region.

From the diagram, we can observe:

  • The larger square PQRSPQRS has equal sides, and the side length of PQPQ (or PSPS) is 10 meters (from point SS to RR).
  • The smaller rectangle PNMLPNML has dimensions of 5 meters along PQPQ and 6 meters along PSPS, meaning PN=5PN = 5 meters and PL=6PL = 6 meters.
  • The colored region being fenced seems to encompass the portion of PQRSPQRS minus the small rectangular region PNMLPNML.

Step-by-step approach:

  1. The fence follows the boundaries of the L-shaped region formed by subtracting the rectangle from the square.
  2. To find the total length of the fencing needed, sum the sides along which the fence is constructed.
  • Side LL to SS = 6 meters
  • Side SS to JJ = 6 meters (along SRSR)
  • Side JJ to KK = 10 meters
  • Side KK to QQ = 55 meters

Total length of fencing:

The perimeter is 6+6+10+5=276 + 6 + 10 + 5 = 27 meters.

Cost:

The cost of fencing is RM 40 per meter. Therefore, the total cost is: Total cost=27×40=RM 1080\text{Total cost} = 27 \times 40 = \text{RM } 1080

Thus, Susan must pay RM 1080 to fence the region.

Would you like a more detailed explanation of any part of the solution?

Here are five related questions to expand on this:

  1. How do you calculate the perimeter of irregular regions?
  2. What is the formula for the perimeter of a square and rectangle?
  3. If the cost per meter increases, how would that affect the total fencing cost?
  4. How would the problem change if the rectangular region was also fenced?
  5. What methods can be used to calculate the area of the fenced region?

Tip: Always ensure you double-check measurements and unit conversions in problems involving geometry to avoid simple mistakes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Area Calculation

Formulas

Perimeter of irregular shapes: sum of individual sides
Cost = Length × Rate per meter

Theorems

Perimeter theorem for squares and rectangles

Suitable Grade Level

Grades 7-9