top of a raised platform is in the shape of a regular octagon as shown in the figure, find the area of the octagon.
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Upper part is in the shape of trapezium. This is mirrored in the lower part as well. So area of two trapeziums added to the area of middle rectangular portion will be equal to the area of the octagon.
The base of the triangle runs from the base of the perpendicular to the edge of the octagon. This can be done by Pythagoras Theorem.
5(square) + 4(square)
25-16=9
Base = 3
The upper parallel side of the trapezium = 11 - 6 =5cms
As it is regular octagon, the upper parallel side = side of the octagon = 5cms
Area of trapezium = 1/2 * sum of parallel sides * perpendicular distance
=1/2*11*5=55/2
Area of two trapeziums = 55 square cms
Area of rectangle = Length * Breadth
=11*5=55
Therefore, area of the octagon = 55 + 55 = 110 square cms.
Hope the answer helps you... :)
The base of the triangle runs from the base of the perpendicular to the edge of the octagon. This can be done by Pythagoras Theorem.
5(square) + 4(square)
25-16=9
Base = 3
The upper parallel side of the trapezium = 11 - 6 =5cms
As it is regular octagon, the upper parallel side = side of the octagon = 5cms
Area of trapezium = 1/2 * sum of parallel sides * perpendicular distance
=1/2*11*5=55/2
Area of two trapeziums = 55 square cms
Area of rectangle = Length * Breadth
=11*5=55
Therefore, area of the octagon = 55 + 55 = 110 square cms.
Hope the answer helps you... :)
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Hope it helps you.................
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