Question

Question #c9a9a

Answer 1

`6`

Explanation:

As shown in Fig 1, `ABCDEF` is a regular hexagon.
A regular hexagon can be divided into 6 equilateral triangles.
Let `A_e` be the area of each equilateral triangle and `A_h` be the area of the hexagon.
`=> A_h=6A_e`
`OABC` is a rhombus consisting of two equilateral triangles,
Area `OABC=2A_e`,
Diagonal `AC` divides the rhombus into two congruent isosceles triangles, `DeltaABC, and DeltaAOC`
`=>` Area `DeltaABC=A_e`
Area `DeltaBCG=` Area`ABC=A_e=1/6A_h`

As shown in Fig 2,
the rectangle mainly consists of hexagons placed side by side.

Let `a` be the area of one regular hexagon in the rectangle.
`=>` Total area `A_t= (10+4*1/2+8*1/6)a=(40a)/3`

Given that the area of the rectangle is `80` sq. ft
`=> A_t=80`
`=> (40a)/3=80`
`=>` area of one hexagon `a=(80*3)/40=6` sq. ft.