Question

Find the surface area of a football cover made of 12 regular pentagon and 20 regular hexagons. Each side is 6cm.

Answer 1

Answer:

Area of regular pentagon

$\frac{1}{4} \sqrt{5(5 + 2 \sqrt{5}) {a}^{2} }$

Area of regular hexagon

$\frac{3 \sqrt{3} }{2} a {}^{2}$

Whre a = side of the regular pentagon or regular hexagon

Putting the value of a= 6 cm

Area of 1 pentagon = 61.94 sq.cm

Area of 1 hexagon = 93.53 sq.cm

Total area of football cover,

= (12×61.94 + 20×93.53) sq.cm

= (743.28 + 1870.6) sq.cm

= 2613.88 sq.cm