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The larger circle has diameter = 4, therefore the radius is 2, and the area is π x 2^{2} = 4π.
The smaller circle has diameter = 2, therefore the radius is 1, and the area is π x 1^{2} = π.
Therefore the shaded area is 4π  π = 3π ≈ 9.42.
Circle
The area of a circle is π x Radius^{2}.
The circle with diameter 3.1 has a radius of 1.55 and an area of π x 1.55^{2} = 7.55.
The circle with diameter 3.5 has a radius of 1.75 and an area of π x 1.75^{2} = 9.62 (** closest match).
The circle with diameter 3.9 has a radius of 1.95 and an area of π x 1.95^{2} = 11.95.
Square
The area of a square is Side x Side.
The square with side 3.1 has an area of 3.1 x 3.1 = 9.61 (** closest match).
The square with side 3.5 has an area of 3.5 x 3.5 = 12.25.
The square with side 3.9 has an area of 3.9 x 3.9 = 15.21.
Triangle
The area of a triangle is ½ x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is Sqrt(3) x Base^{2} ÷ 4.
The triangle with side 3.9 has an area of Sqrt(3) x 3.9 x 3.9 ÷ 4 = 6.59.
The triangle with side 4.3 has an area of Sqrt(3) x 4.3 x 4.3 ÷ 4 = 8.01.
The triangle with side 4.7 has an area of Sqrt(3) x 4.7 x 4.7 ÷ 4 = 9.57 (** closest match).
Puzzle 4
Starting in the bottom left corner and moving either up or right, one square at a time, adding up the numbers along the way, what is the largest sum which can be made once you have reached the top right corner?
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