The larger circle has diameter = 40, therefore the radius is 20, and the area is π x 202 = 400π.
The smaller circle has diameter = 20, therefore the radius is 10, and the area is π x 102 = 100π.
Therefore the shaded area is 400π – 100π = 300π ≈ 942.
Circle
The area of a circle is π x Radius2.
The circle with diameter 31 has a radius of 15.5 and an area of π x 15.52 ≈ 755.
The circle with diameter 35 has a radius of 17.5 and an area of π x 17.52 ≈ 962 (closest match).
The circle with diameter 39 has a radius of 19.5 and an area of π x 19.52 ≈ 1195.
Square
The area of a square is Side x Side.
The square with side 31 has an area of 31 x 31 = 961 (closest match).
The square with side 35 has an area of 35 x 35 = 1225.
The square with side 39 has an area of 39 x 39 = 1521.
Triangle
The area of a triangle is 1/2 x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is √3 x Base2 ÷ 4.
The triangle with side 39 has an area of √3 x 39 x 39 ÷ 4 ≈ 659.
The triangle with side 43 has an area of √3 x 43 x 43 ÷ 4 ≈ 801.
The triangle with side 47 has an area of √3 x 47 x 47 ÷ 4 ≈ 957 (closest match).
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Puzzle 24
Start in the bottom left corner and move either up or right, one square at a time, adding up the numbers. What is the largest total you can make?
1
4
2
2
1
2
4
3
1
3
4
3
2
1
4
2
1
2
1
2
2
3
3
1
4
1
3
1
2
1
3
1
4
3
4
2
2
1
1
1
1
3
3
4
2
3
2
2
Note: this puzzle is not interactive, and the numbers cannot be clicked.
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