Surface Area and Housing Inequities Vocabulary Review

How to Use

• Review each vocabulary word before your quiz.
• Study the math, real-life, and fairness examples to understand how geometry helps uncover housing inequalities.
• Keep this sheet in your Equity in Numbers Student Journal to refer back when exploring real-world community design.
• Remember: Math isn’t just about numbers—it’s about fairness, comfort, and dignity for everyone.

Surface Area

• Definition: The total area of all the outer surfaces of a 3D shape.
• Math Examples:
  • ( SA = 2lw + 2lh + 2wh )
  • For a building 100 ft × 40 ft × 60 ft → ( SA = 2(100×40) + 2(100×60) + 2(40×60) = 24,800 , \text{ft}² )
• Real-Life Example: Finding the amount of wall and roof space on an apartment building.
• Fairness Example: Larger surface areas often mean more windows, light, and air—important for health and comfort in homes.

Rectangular Prism

• Definition: A 3D solid with six rectangular faces, such as a building or box.
• Math Examples:
  • Dimensions: ( l = 80 , ft, , w = 30 , ft, , h = 50 , ft )
  • ( SA = 2(80×30) + 2(80×50) + 2(30×50) = 15,800 , ft² )
• Real-Life Example: Representing an apartment tower as a rectangular prism to calculate materials or design features.
• Fairness Example: Comparing prisms helps visualize how low-income housing may have smaller, tighter spaces than higher-income housing.

Length, Width, and Height

• Definition: The three measurements used to calculate surface area or volume of rectangular solids.
• Math Examples:
  • ( l = 120 , ft, , w = 50 , ft, , h = 40 , ft ) → substitute into formula for ( SA ).
• Real-Life Example: Measuring building dimensions for construction or renovation plans.
• Fairness Example: Variations in height or width can show why some apartments feel cramped while others are open and airy.

Formula

• Definition: A mathematical equation used to solve a specific type of problem.
• Math Examples:
  • ( SA = 2lw + 2lh + 2wh ) (surface area)
  • ( A = l × w ) (area of one face)
• Real-Life Example: Builders and architects use formulas to calculate how much paint, glass, or siding they’ll need.
• Fairness Example: Applying the same formula across neighborhoods ensures accurate, data-based comparisons in housing equity studies.

Square Units (ft²)

• Definition: The units used to measure surface area; each square unit represents a 1 ft × 1 ft surface.
• Math Examples:
  • ( 24,800 , ft² ) = the total area of all outer building surfaces.
• Real-Life Example: Estimating how much exterior space needs to be painted or insulated.
• Fairness Example: Using consistent square units ensures fair comparisons of building sizes between different communities.

Compare

• Definition: To examine two or more quantities to identify similarities or differences.
• Math Examples:
  • Low-income tower: ( 15,800 , ft² ); High-income condo: ( 28,000 , ft² ).
• Real-Life Example: Comparing surface area of different apartment buildings.
• Fairness Example: Comparing buildings helps reveal inequities in access to space, sunlight, and ventilation across neighborhoods.

Equity

• Definition: Fair access to opportunities, comfort, and well-being for all people.
• Math Examples:
  • Using geometry to compare building designs for fairness.
• Real-Life Example: Ensuring that both low- and high-income neighborhoods have housing that promotes safety and comfort.
• Fairness Example: Math provides clear data for city planners and communities to advocate for equitable living conditions.

Design

• Definition: The plan or structure that shapes how something looks and functions.
• Math Examples:
  • Using dimensions to draw or build proportional housing models.
• Real-Life Example: Architects use surface area calculations to design windows, doors, and outer walls.
• Fairness Example: Inclusive design ensures housing meets the needs of all families—balancing aesthetics, comfort, and sustainability.

Housing Inequity

• Definition: Unequal access to safe, comfortable, and healthy living spaces across communities.
• Math Examples:
  • Comparing total surface area per family to identify overcrowded conditions.
• Real-Life Example: Some communities have tall, compact apartments with less light, while others have spacious, sunlit condos.
• Fairness Example: Surface area helps quantify inequity—turning abstract fairness issues into measurable, fixable data.

Comfort

• Definition: The quality of having adequate space, light, and air for healthy living.
• Math Examples:
  • Larger surface area → more windows → more ventilation.
• Real-Life Example: Apartments with higher surface areas per unit allow better airflow and natural light.
• Fairness Example: Math highlights how physical comfort can depend on housing design and resource allocation.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Surface Area	Measures all outer surfaces	Shows living space, light, and air differences
Rectangular Prism & Formula	Models building design	Reveals inequities in building comfort
Compare & Equity	Uses data to analyze fairness	Promotes design justice and housing reform
Design & Comfort	Connects geometry to experience	Supports livable, healthy environments for all