Answer:
Area covered by wiper=area of arc(A0D)+area of traingleAOB+area of arc(BOC)
We know AO and OB are wipers,whose lengths are 1.5
In ∆ABC
AB^2+BC^2=AC^2
(1.5√3)^2+(1.5)^2=(AC)^2
2.25×3+2.25=(AC)^2
2.25×4=AC^2
AC=3
Also AO=1.5
similarly using Pythagoras theorem in ∆OBC
we get
OC=1.5
this shows that point O is the bisector of diagonal AC
so,AO=OC
also from property of rectangle we know that, diagonal bisects each other equally
so,O will also be the bisector of diagonal BD
hence OB=OD=1.5
AC=BD (property of triangle)
AC/2=BD/2
OB=OC,hence OB=OC=OD=OA=1.5=AD=BC
Hence OAD will be an equilateral triangle
so
angle OAD=60
similarly angleOBC=60
area of sector=angle of that sector ×area of circle/360
area of arc(AOD)+arc(BOC)=60/360 ×3.14 ×1.5×1.5 +60/360 ×3.14×1.5×1.5
=2×(60/360)×1.5×1.5
area of triangleAOB=area of rectangle/4 (diagonal divides the rectangle in 4 equal parts)
area of triangle=1.5×1.5√3/4
=>1.5×2.6/4=3.90/4
=0.975 or 0.98(approx)
Area covered by wiper=.98+2×60/360 ×3.14×1.5×1.5
=.98+0.75×3.14=2.35+0.97
=2.35+.98
Percentage of area of windshield covered by wiper=3.3×100/3.9=84.61
hence percentage of area of windshield covered by wiper is 85percent(approx)
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