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Why is radius greater than apothem?
In a regular polygon, the apothem is a line from the centre to the mid-point of one of the flat sides. The radius is a line from the centre to a corner, which is longer.
What is the area of a regular hexagon with a side length of 2 centimeter and an apothem length of 10.4 centimeters?
Such a hexagon is impossible. A regular hexagon with sides of 2 cm can have an apothem of sqrt(3) cm = approx 1.73.It seems you got your question garbled. A regular hexagon, with sides of 2 cm, has an area of 10.4 sq cm. If you used your measurement units properly, you would have noticed that the 10.4 was associated with square units and it had to refer to an area, not a length.
What is Area of a regular pentagon with radius of 5.1 and side of 7.5?
A regular pentagon with a radius (apothem) of 5.1 units cannot have sides of 7.5 units and, conversely, a regular pentagon with sides of length 7.5 units cannot have a radius of 5.1 units. The figure is, therefore, impossible.
What is the area of a hexagon with a side of 10 inches and an apothem of 8 inches?
The question cannot be answered. A regular hexagon with sides of 10 inches would have apothems of 10/sqrt(2) = 7.071 inches. Therefore the hexagon cannot be regular. And, since the hexagon is irregular, there is not enough information to answer the question.
What is the length of the apothem of a regular hexagon with 10 cm sides?
The hexagon will consist of 6 equilateral triangles of 3 equal sides of 10 cm and the apothem will divide the triangle into 2 right angle triangles with a base of 5 and an hypotenuse of 10 and so by using Pythagoras' theorem the height of the triangle which is the apothem works out as 5 times square root of 3 or about 8.66 cm rounded to 2 decimal places.
