Math Problem Statement

Suppose that one of the rooms at your local meetinghouse has a surface area of 59 square yards (yd2). Use the fact that 1 yard = 0.9144 m to convert this measurement to square meters (m2). Round your answer to the nearest tenth. Do not type the units in the space below.

Solution

To convert 59 square yards (yd²) to square meters (m²), we first need to use the conversion factor for linear measurements (1 yard = 0.9144 meters). However, since we are working with square yards, we need to square this conversion factor.

Steps:

  1. Square the conversion factor: 1yd2=(1yard)2=(0.9144m)2=0.91442m21 \, \text{yd}^2 = (1 \, \text{yard})^2 = (0.9144 \, \text{m})^2 = 0.9144^2 \, \text{m}^2 0.91442=0.8361m2/yd20.9144^2 = 0.8361 \, \text{m}^2/\text{yd}^2

  2. Convert 59 yd² to m²: 59yd2×0.8361m2/yd2=49.3m259 \, \text{yd}^2 \times 0.8361 \, \text{m}^2/\text{yd}^2 = 49.3 \, \text{m}^2

Thus, 59 square yards is approximately 49.3 square meters.


Would you like more details on how this conversion works, or do you have any further questions?

Related Questions:

  1. How do you convert square inches to square centimeters?
  2. What is the relationship between square meters and hectares?
  3. How can you convert cubic yards to cubic meters?
  4. What is the difference between linear and square unit conversions?
  5. How would you convert an area measured in feet squared to miles squared?

Tip:

When converting between square units, always square the linear conversion factor before multiplying.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Area Conversion
Squaring a Conversion Factor

Formulas

Area conversion formula: Area (m²) = Area (yd²) × (Conversion factor)^2

Theorems

Unit Conversion Theorem

Suitable Grade Level

Grades 6-8