Question

# A drawing of a portion of a wall that is to be covered with wallpaper is given below. If the wallpaper is sold in rolls that are 0.5 ft wide and 30 ft long, how many such rolls will be needed to cover the wall?

A
12
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B
18
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C
16
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D
15
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Solution

## The correct option is A 12 Overall area of the wall = Area of ΔADC+Area of ADEB+ Area of BEF In ΔADC, Base, b=5 ft, height, h=12 ft Area of ΔADC=12×5×12=5times6=30ft2 BEF has the same dimensions as ΔADC, Area ofΔBEF= Area of ΔADC=30ft2 In rectangle ABDE, Length,l=10ft width,w=12ft Area of ADEB=l×w=10×12=120ft2 Overall area =30+30+120=60+120=180ft2 Thus, wallpaper of an area of 180ft2 is needed to cover the wall. Area of each roll of wallpaper =0.5×30=15ft2 Number of rolls =TotalareaofwallAreaofeachroll=18015=12 Thus, 12 rolls will be needed to cover the wall.

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