Math Problem Statement

fill in the table

Solution

Let's fill in the table based on the given data and proper unit conversions.

Row 4:

  • Dimensions: 6 cm and 12 dm
  • Given Area: 96 dm²
  1. Convert 6 cm to decimeters (dm): 6cm=0.6dm6 \, \text{cm} = 0.6 \, \text{dm}

  2. Calculate the area using the formula: Area=length×width=0.6dm×12dm=7.2dm2\text{Area} = \text{length} \times \text{width} = 0.6 \, \text{dm} \times 12 \, \text{dm} = 7.2 \, \text{dm}^2

Since the calculated area (7.2 dm²) doesn't match the given area (96 dm²), it seems the given area was intended to be 7.2 dm² but could be misprinted.

Row 5:

  • Dimensions: 8 m and 7 m
  • Given Area: 168 m²
  1. Calculate the area using the formula: Area=length×width=8m×7m=56m2\text{Area} = \text{length} \times \text{width} = 8 \, \text{m} \times 7 \, \text{m} = 56 \, \text{m}^2

Given the significant difference, it's likely that the area should be 56 m² instead of 168 m².

Filled Table

RowLength (Unit)Width (Unit)Area (Unit)
46 cm (0.6 dm)12 dm7.2 dm²
58 m7 m56 m²

Please confirm or correct any of these if necessary. Would you like any further exploration or another calculation? Here are five questions to consider:

  1. How would the area calculation change if both dimensions in Row 4 were provided in centimeters?
  2. What would the area be if the width in Row 4 were 12 cm instead of 12 dm?
  3. If the area in Row 5 was indeed 168 m², what would the necessary dimensions be to achieve this?
  4. How can you verify the correctness of measurements and units in similar problems?
  5. What might cause such discrepancies between calculated and given areas?

Tip: When filling in tables or solving problems with measurements, always double-check the consistency of units to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Unit Conversion
Area Calculation

Formulas

Area of a rectangle: length × width

Theorems

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Suitable Grade Level

Grades 6-8