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Area, Volume, and Energy Calculations in Buildings

Abdul a

aStudent

ABSTRACT:

Accurately measuring the exact dimensions of buildings, rooms & floors is crucial for measuring

energy use in buildings will help in designing better energy efficiency designs. Energy se!ntensity "E!# calculations used by floor is used to estimate total energy use by building.

Calculating the floor space area and useful $olume per floor will further assist in designing

efficient heating systems and lighting re%uirement of building. his report focuses oncalculations of regular and irregular floor space areas and different shapes and $olume

calculations in buildings.

Area, Volume, and Energy Calculations in Buildings Page 1


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INTRODUCTION

Calculation of Regular areas in a floor plan: Area is a measure of how much spacethere is inside a shape. Areas of S%uares and 'ectangles "and parallelograms#. he simplest "and

most commonly used# area calculations are for s%uares and rectangles. o find the area of a

rectangle multiply its height by its width. (or a s%uare you only need to find the length of one of the sides "as each side is the same length# and then multiply this by itself to find the area. his is

the same as saying length) or length s%uared. !t is good practice to chec* that a shape is actually a

s%uare by measuring two sides. (or example the wall of a room may loo* li*e a s%uare but whenyou measure it you find it is actually a rectangle.

+ften, in real life, shapes can be more complex. (or example, imagine you want to find the area

of a floor, so that you can order the right amount of carpet. A typical floorplan of a room may not

consist of a simple rectangle or s%uare



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Exaple: !n this example, and other examples li*e it, the tric* is to split the shape into se$eral

rectangles "or s%uares#. !t doesn-t matter how you split the shape any of the three solutions will

result in the same answer. Solution and ) re%uire that you ma*e two shapes and add their areastogether to find the total area. (or solution / you ma*e a larger shape "A# and subtract the

smaller shape "B# from it to find the area. Another common problem is to the find the area of a

border 0 a shape within another shape. his example shows a path around a field 0 the path is )mwide. Again, there are se$eral ways to wor* out the area of the path in this example. 1ou could

$iew the path as four separate rectangles, calculate their dimensions and then their area and

finally add the areas together to gi$e a total. A faster way would be to wor* out the area of thewhole shape and the area of the internal rectangle. Subtract the internal rectangle area from the

whole lea$ing the area of the path.

he area of the whole shape is 2m 3 4m 5 24m ). 6e can wor* out the dimensions of the

middle section because we *now the path around the edge is )m wide. he width of the wholeshape is 2m the width of the path across the whole shape is 7m ")m on the left of the shape and

)m on the right#. 2m 7m 5 )m. 8o the same for the height 4m )m )m 5 2m. So we ha$e

calculated that the middle rectangle is )m 3 2m. he area of the middle rectangle is therefore)m 3 2m 5 9)m). (inally we ta*e the area of the middle rectangle away from the area of the

whole shape. 24 9) 5 ::m). he area of the path is ::m)

Calculation of Irregular areas in a floor plan: A parallelogram is a foursided shape

with two pairs of sides with e%ual length 0 by definition a rectangle is a type of parallelogram.;owe$er, most people tend to thin* of parallelograms as foursided shapes with angled lines, as

illustrated here. he area of a parallelogram is calculated in the same way as for a rectangle"height 3 width# but it is important to understand that height does not mean the length of the

$ertical "or off $ertical# sides but the distance between the sides. (rom the diagram you can see

that the height is the distance between the top and bottom sides of the shape not the length of the



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side. hin* of an imaginary line, at right angles, between the top and bottom sides. his is the

height.

Areas of Triangles

!t can be useful to thin* of a triangle as half of a s%uare or parallelogram. Assuming you *now

"or can measure# the dimensions of a triangle then you can %uic*ly wor* out its area.

he area of a triangle is "height 3 width# < ). !n other words you can wor* out the area of a

triangle in the same way as the area for a s%uare or parallelogram =ust di$ide your answer by ).he height of a triangle is measured as a rightangled line from the bottom line to the >apex- "top

point# of the triangle.



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Exaple:

he area of the three triangles in the diagram abo$e is the same.

Each triangle has a width and height of /cm.

he area is calculated"height 3 width# < ) / 3 / 5 ?

? < ) 5 7.@

he area of each triangle is 7.@cm

)

.

!n reallife situations you may be faced with a problem that re%uires you to find the area of a

triangle, such as

1ou want to paint the gable end of a barn. 1ou only want to $isit the decorating store once to getthe right amount of paint. 1ou *now that a litre of paint will co$er 4)m of wall. ;ow much

paint do you need to co$er the gable end

1ou need three measurementsA he total height to the apex of the roof.

B he height of the $ertical walls.

C he width of the building.

!n this example the measurements areA ).7m

B 2.2m

C .2m

he next stage re%uires some additional calculations. hin* about the building as two shapes, arectangle and a triangle. (rom the measurements you ha$e you can calculate the additional

measurement needed to wor* out the area of the gable end.

easurement 8 5 ).7 0 2.28 5 @.:m

1ou can now wor* out the area of the two parts of the wall

Area of the rectangle part of the wall 2.2 3 .2 5 92.@2m)

Area of the triangular part of the wall

"@.: 3 .2# < ) 5 //.27m)

Add these two areas together to find the total area

92.@2 //.27 5 4.)m)



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As you *now that one litre of paint co$ers 4m) of wall so we can wor* out how many litres we

need to buy

4.) < 4 5 .4) litres.!n reality you may find that paint is only sold in @ litre or litre cans, the result is =ust o$er

litres. 1ou may be tempted to round down to litres but, assuming we don-t water down the

paint, that won-t be %uite enough. So you will probably round up to the next whole litre and buytwo @ litre cans and two litre cans ma*ing a total of ) litres of paint. his will allow for any

wastage and lea$e most of a litre left o$er for touching up at a later dateD

Areas of Circles:

!n order to calculate the area of a circle you need to *now its radius or diameter. he diameter of

a circle is the length of a straight line from one side of the circle to the other that passes through

the central point of the circle. he diameter is twice the length of the radius "8ia 5 radius 3 )#.

he radius of a circle is the length of a straight line from the central point of the circle to its edge.he radius is half of the diameter. "radius 5 diameter < )#. 1ou can measure the diameter or

radius at any point around the circle 0 the important thing is to measure using a straight line that passes through "diameter# or ends at "radius# the centre of the circle. !n practice, when measuringcircles it is often easier to measure the diameter, then di$ide by ) to find the radius. 1ou need the

radius to wor* out the area of a circle, the formula is

circle area 5 ' ).

his means

5 Fi is a constant that e%uals /.7). ' 5 is the radius of the circle.

') "radius s%uared# means radius 3 radius.

herefore a circle with a radius of @cm, has an area of /.7) 3 @ 3 @ 5 9:.@@cm).A circle with a diameter of /m has an area

(irst we wor* out the radius "/m < ) 5 .@m#

hen apply the formula')

/.7) 3 .@ 3 .@ 5 9.42?@.

he area of a circle with a diameter of /m is 9.42?@m ).

Different s!apes and "olues calculations in buildings: +ne important aspect of your structure is how much useable space it has. Volume is a measure of how much space your



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building contains. here are two main shapes that a building can ha$e, the rectangular prism and

the pyramid. 8o not worry if your building does not form a pyramid, because they are not

re%uired "but could be useful for increasing your building $olume#. Below are some examples of how you can calculate your building $olume.

Case stud# for areas and "olues in Buildings:

his example pulls on much of the content of this page for sol$ing simple area problems.



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his is the 'uben . Ben=amin ;ouse in Bloomington !llinois, listed on he nited States

Gational 'egister of ;istoric Flaces "'ecord Gumber /92@??#.

his example in$ol$es finding the area of the front of the house, the wooden slatted part 0

excluding the door and windows. he measurements you need are

A 0 ?.9mB 0 9.2m

C 0 :.:m

8 0 7.@mE 0 )./m

( 0 ).9m

H 0 .)m

; 0 .4m

Assumptions

. All measurements are approximate.

). here is no need to worry about the border around the house 0 this has not been included

in the measurements./. 6e assume all rectangular windows are the same siIe.



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7. he round window measurement is the diameter of the window.

@. he measurement for the door includes the steps.

Area of t!e $ooden slatted part of t!e !ouse:

(irst, wor* out the area of the main shape of the house 0 that is the rectangle and triangle that

ma*e up the shape.

he main rectangle "B 3 C# 9.2 3 :.: 5 22.::m).he height of the triangle is "A 0 B# ?.9 0 9.2 5 )..

he area of the triangle is therefore "). 3 C# < ). ). 3 :.: 5 :.7:. :.7: < ) 5 ?.)7m).

he combined full area of the front of the house is the sum of the areas of the rectangle andtriangle

22.:: ?.)7 5 92.)m).

Gext, wor* out the areas of the windows and doors, so they can be subtracted from the full area.

he area of the door and steps is "8 3 E# 7.@ 3 )./ 5 4./@m).he area of one rectangular window is "H 3 (# .) 3 ).9 5 /.)7m).

here are fi$e rectangular windows. ultiply the area of one window by @.

/.)7 3 @ 5 2.)m). "the total area of the rectangular windows#.he round window has a diameter of m its radius is therefore 4.@m.

sing ') wor* out the area of the round window /.7) 3 4.@ 3 4.@ 5. 4.9:@@m).

Gext add up the areas of the door and windows."door area# 4./@ "rectangle windows area# 2.) "round window area# 4.9:@@ 5 )9.//@@

(inally, subtract the total area for the windows and doors from the full area.

92.) 0 )9.//@@ 5 7:.9:7@

he area of the wooden slatted front of the house, and the answer to the problem is 7:.9:7@m).1ou may want to round the answer up to 7:.:m) or 7?m).

RE%ERENCES:

JK Building Energy se'LhttpMMsustainabilitywor*shop.autodes*.comMbuildingsMmeasuringNbuildingN

energyNuseOsthash.wyF:lHV.dpuf

J)K Areas Calculation'L httpMMwww.s*illsyouneed.comMnumMarea.htmlOixII7)A+fVAxP

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