Question

Find the area of a hexagonal field having the sides of 16 m each. (Diagonals divide the regular hesa ist congruent equilateral triangles)​

Answer 1

Step-by-step explanation:

A regular hexagon is made up on 6 Equilateral Triangles

Altitude of the Equilateral Triangle is worked out as under:

As per Pythegoras theorem, (1/2 base) Square + Altitude Square = Diagonal Square

Therefore, Altitude square = Diagonal square - (1/2 base) square= 16 square - 8 square = 256 – 64 and

Altitude Square = 256–64 = 192

Hence, Altitude = Square root of 192 = 13.86 meters

Area of one Equilateral Triangle = 1/2 Base x Altitude = 1/2 x 16 x 13.86= 8 x 13.86 =110.88 meter square

Total area of Hexagon = Area of 6 Equilateral Triangles = 6 x 110.88= 665.28 sq. mts.

Answer: Area of Regular Hexagon of 16 meter side = 665.28 square meters

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