(re)learning the basics feet and inches perimeter area volume proportions

(Re)Learning The Basics

• Feet and Inches

• Perimeter

• Area

• Volume

• Proportions

WHY IS THIS IMPORTANT?

Units of Measure

• “Customary” – US only, used in architecture

• Metric – Global, also sometimes used in US for engineering

Measuring Vocabulary

• Customary– Inch, Foot (=12 inches), Yard (=3 Feet), Mile

(=5280 Feet)– Measures less than one inch are in fractions ½,

¼, 1/8, 1/16, 1/32. 1/64

• Metric– Meter, Kilometer (1000 meters)– Less than one meter:

• Decimeter (1/10), Centimeter (1/100), Millimeter (1/1000), etc.

Activity (Part 1: To Be Handed In)

• Add 10’6” and 4’9”

• Subtract 2’ 8” from 13’

• How many inches in a mile

• How many yards in a mile

• How many inches in a 1.5 yards

Perimeter of a rectangle• From math, perimeterof a rectangle is:

– 2 x length + 2 x width– Ex. A room with l = 10’ and w = 12’ has

perimeter of 44’• What is the perimeter of a room with

dimensions:– 11’4” x 10’8”– 8’3” x 12’7”– 120’3” x 70’5’

Perimeter of an Arbitrary Figure

• Perimeter is the sum of the side lengths

• Ex: Side lengths clockwise from point A are 4’5”, 1’5”, 8”, 1’5”, 5’1”, 3’9”. What is perimeter?

• What if each side is halved?

A

Area of a Rectangle• From math, area of a rectangle is:

– length x width– Ex. A room with l = 10 and w = 12 has Area =

120• Converting feet/inches to decimal feet:

– 12’5” = 12 + 5/12 feet = 12.42 feet =12.42’• General calculation of area of a room

– Ex. A room with l = 12’5” and width = 10’2” has area of (12+5/12) x (10+2/12) = 126.24 square feet

Volume of a Rectangular Solid• From math, volume of a rectangular solid is:

– length x width x height– Ex. A room with l = 10 and w = 12 and 8 foot

ceilings has a volume of 10 x 12 x 8 = 960 cubic feet

– Ex. A room with l = 12’2” and w = 10’ 4” and 9 foot ceilings has a volume of (12+2/12) x (10 + 4/12) x 9 = 1131.5 cubic feet

• Common decimals to know:

• 3” = ¼ foot = .25 feet, 4”, 6”, 8”, 9”

Practice

• What are the fractional and decimal equivalents of 3”, 6”, 9”, 4”, 8”

• Find the perimeters of the following rooms– L = 10, w = 10– L = 8’6”, w = 12’ 6”– L = 17’2”, w = 19’5”

• Find the area of each if these rooms

• Find the volumes of the above rooms at ceiling heights of 8’6”, 9’, and 10’

Ratios

• Compares/converts one unit of measure to another:– Ex: a map, 1” equals one mile then ratio is

1”/1 mile or 1mile/1” or 1”:1 mile or 1 mile: 1”– Ex: Busses required for the band…– Ex: Computers per student in our class

Practice

• Convert from 10 feet to inches using a proportion to convert, show work

• Convert 10 inches to cm using the conversion factor of 2.54 cm/inch

How to read an Architect’s Scale

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What is an Architect’s scale?

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A triangular shaped instrument used for making or measuring scaled drawings such

as blueprints or floor plans.

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Scales can be made of wood, plastic, or aluminum.

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The scale can be read from left to right and right to left.

1/8” scale would be read from left to right and the ¼” scale would be read from right to left.

What does “drawn to scale” mean?

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For example, one-fourth inch (¼”) on the plan may represent one foot (1’) in the real world.

On a scaled drawing, a small measurement is used to represent a large measurement.

One word…..Two different meanings

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2. The unit of measurement that plans are proportionally drawn to

¼ ” = 1’

1. The actual instrument used for drawing and measuring

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Commercial buildings may be drawn at 1/8” = 1’ if they are too large to fit on the desired sheet size at ¼” = 1’.

Floor plans for residential structures are usually drawn at ¼” = 1’.

Step 1Determine the drawing scale.

Example 1

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Step 1Determine the drawing scale.

Example 2

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Step 1Determine the drawing scale.

Example 3

Step 2Find the matching number on the architect’s

scale.

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Step 3Place the scale on the print. Place the mark

above the zero at the beginning of the line to be measured.

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Step 4, Using the scale to draw.

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To drawn your own prints, determine the length of the object to be drawn, then scale it down

accordingly using the architect’s scale.

For example, using the 1/8”= 1’ example, a wall 20 feet in length would become 20/8 inches, or 2 1/2 inches on the blueprint.