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The area of the left over wood is
Area of the kite
perimeter of the kite
The area of the left over wood is given by
= area of the circle - area of the pentagon
area of the circle
= pi * r^2
= pi * 5^2
= 78.54 square cm
area of the pentagon
= 5/2 * a * 5
solving for a
360 / 5 = 72
72 / 2 = 36
cos 36 = a / 5
a = 5 cos 36 = 4
area of the pentagon = 5/2 * 4 * 5 = 50 sq cm
left over wood = 78.54 - 50 = 28.54 square cm
Area and perimeter of kite
area of kite = product of the two diagonals
length of one of the diagonals = 2 * KT = 2 * 12 = 24 cm.
The second diagonal
tan 30 = KT / x
x = 12 / tan30 = 20.78
the length = 12 + 20.78 = 32.78
area of the kite = 32.78 * 24 = 786.72 square cm
perimeter of the kite
= addition of the sides = 2(shorter side + longer side)
Using Pythagoras rule
shorter side = √(12² + 12²) = 16.97
longer side = √(20.78² + 12²) = 24
perimeter = 2 (16.97 + 24) = 81.94 cm
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