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User YusufUMS
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1 Answer

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Solution:

Case: Area

Given: A house to be painted

Method/ Final answers

a) Find the area of the garage to be painted.

(i) Front.

A = l X w - Garage door area

l= 15 ft, b= 10-4 gives 6ft

A= 15 X 6 - (10 X 7)

A= 90 - 70

A= 20 square feet

ii) Side

A= l X w

A= 6 X 5

A= 30 square feet

iii) The sum of areas

A= 20 + 30

A= 50 square feet

b) Area of the painted region around windows 5 and 6.

Since 12 in = 1 ft

Area of front door converted to feet is (20/3) ft by 3 ft

Areas of windows 5 and 6 converted to feet is 3 ft by (5/3) ft each

A= Area of space - (Area of front door + window 5 + window 6)

A= (30 X 10) - [(20/3) X 3 + 3 X (5/3) + 3 X (5/3)]

A= 300 - [20 + 5 + 5]

A= 300 - 30

A= 270 square feet.

c) Area of the painted region around windows 3

A= Total face - Area of window 3

A= (Rectangle + Parallelogram + Triangle) - Area of window 3

A= [(10 X 4) + (5 X 4) + (0.5 X 4 X 3)] - [1 X (5/3)]

A= [40+20+6] - [5/3]

A= 66 - (5/3)

A= 193/3 square feet

A= 63.33 square feet

d) Area of the region on the second floor with 2 rectangles and the region around window 4

i) region with rectangle 1 from left to right

A= 10 X (15- 6)

A= 10 X 9

A = 90

ii) region with rectangle 2 from left to right

A= 10 X (15- 6)

A= 10 X 9

A = 90

iii) Area of region around window 4

Area of space - area of window

A= 10 X (30-9-12) - [3 X (5/2)]

A= 10 X 9 - (15/2)

A= 82.5.

Total area= 90 + 90 + 82.5

= 262.5 square feet

e) Total area of the painted region (white)

262.5 + 63.33+ 270 + 50

= 645.83 square feet.

f) Additional question

The total cost if it cost $8 per sq ft

645.83 square feet X $8 per sq ft

=$5166.64

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