Solve the following geometry and measurement problems.To help you get started you may wish to employ Pólya’s four problem-solving steps. Remember to check that your final answers make sense and do...

2. (a)
The patio consists of a semi-circle + a square + another semi-circle
Thus, the total area of the patio = area of the semi-circle + area of the square + area of the other semi-circle
Area of the square = (side)2
= (6 m)2
= 36 m2
From fig., the diameter of the semi-circle = side of the square = 6 m
The radius of the semi-circle (r) = diameter of the semi-circle/2 = 3 m
Area of the semi-circle = Area of circle / 2 = (л r2 )/2
= (3.14 × 9)/2
= 14.13 m2
Thus, total area of the patio = 14.13 m2 + 36 m2 + 14.13 m2
= 64.26 m2
2. (b)
It is known that the concrete of the patio is 10 cm thick. We need to calculate that how many cubic meters of concrete are required to make the patio (that is we need to calculate the valume of the patio)
The volume of the patio = area of the patio × thickness of the concrete
= 64.26 m2 × 0.1 m (10 cm = 0.1 m)
= 6.4 m3
So, 6.4 m3 concrete is needed to make a patio in the given shape.
4. (a)
we want to calculate the largest area witch can be enclosed by a 120m long fence.
As we know that for a given perimeter, the shape which has the largest area is the circle.
The shape will be made of the total length of the fence.
Thus, the perimeter of the shape = length of the fence = 120 m
The perimeter of circle 2лr = 120 m (r is the radius of the circle)
r = 60/л m
Area of the circle = л r2
= л...