Question

Find the surface area of a football cover made of 12 regular pentagon and 20 regular hexagons.
( Area of a pentagon of 6 cm Side 61.92 cm ^2)​

Answer 1

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$\bf \scriptsize{Area \: of \: 1 \: pentagon = 61.92 cm^{2} }$

$\bf \scriptsize{Area \: of \: 12 \: Pentagons \: = 12× \: 61 . 92}$

$\bf \scriptsize{Area \: of \: one \: side\: hexagons = \: 6 \: cm}$

$\bf \scriptsize{Hexagon \: Contains \: 6 \: equilateral triangles ,}$

$\bf \scriptsize{Area \: of \: a \: Equilateral \: triangle = \frac{ \sqrt{3} }{4}(a)^{2}} \\ \\ \bf \scriptsize{\implies \frac{ \sqrt{3} }{4} (6)^{2} } \\ \\ \bf \scriptsize{ \frac{1.73 \times 36}{4} = 15.57 \: cm ^{2} }$

$\bf \scriptsize{Area \: of \: hexagon = 6 \: times \: area \: of \: equilateral \: triangles} \\ \bf \scriptsize = 6 \times 15.57 = 93.42 \: cm^{2}$

$\bf \scriptsize{Area \: of \: 20 \: hexagon = 20 \times 93.42} \\ \bf \scriptsize= 1868.40 \: cm^{2}$

$\bf \scriptsize{Area \: of \: football \: cover = Area \: of \: 12 \: pentaons \: + Area \: of \: 20 \: hexagon } \\ \bf \scriptsize=743.04 \times 1868.40 \: cm^{2} \\ \bf \scriptsize = 2611.44 \: cm^{2}$

$\bf \scriptsize \red{Hence , Area \: of \: Football \: = \: 2611.44 \: cm^{2} }$

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