Math Problem Statement

According to the city expansion plan, a plot of 1396 m² consists of two partially overlapping plots, whose combined area is designated for a car parking lot. The area of the first plot is 968 m², and the second plot is 586 m². Calculate the area of the future car parking lot.

Solution

The task in the image is to calculate the area of the future car parking lot based on the given data. Here is a translation of the problem from Lithuanian:

Problem Statement: According to the city expansion plan, a plot of 1396 m² consists of two partially overlapping plots, whose combined area is designated for a car parking lot. The area of the first plot is 968 m², and the second plot is 586 m². Calculate the area of the future car parking lot.

Solution:

  1. Let A=968m2A = 968 \, \text{m}^2 be the area of the first plot.
  2. Let B=586m2B = 586 \, \text{m}^2 be the area of the second plot.
  3. Let T=1396m2T = 1396 \, \text{m}^2 be the total area of the combined plots, which includes the overlap.

The overlap area CC can be found by subtracting the sum of both plots from the total area:

C=A+BT=968+5861396=158m2C = A + B - T = 968 + 586 - 1396 = 158 \, \text{m}^2

Thus, the area of the future car parking lot, which is the total combined area without double-counting the overlap, is:

T=1396m2T = 1396 \, \text{m}^2

Answer: The area of the future car parking lot is 1396 m².

Would you like more details on the solution or have any questions?

Here are some related questions you might find interesting:

  1. What is the significance of understanding overlap areas in real-world applications?
  2. How would the solution change if the total area was not provided?
  3. Can you explain the concept of set theory as it relates to overlapping areas?
  4. How would you calculate the overlap if only partial data were provided for each plot?
  5. What are some methods to visualize overlapping areas in practical scenarios?

Tip: When dealing with overlapping areas, always ensure to account for double-counting, which can often lead to overestimating the total area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area calculation
Overlapping areas

Formulas

C = A + B - T
T = Area of the car parking lot

Theorems

Set theory applied to overlapping areas

Suitable Grade Level

Grades 9-12