Question

Geoff uses hexagonal tiles to create a tessellation pattern in his garden, as pictured below. What is the area of each tile?

5.4 in.
A
about 32 in 2
B. about 76 in 2
about 180 in 2
D
about 64 in 2

Answer 1

B. about 76 in 2

Explanation:

The picture of the question in the attached figure

I will assume that the tile is a regular hexagon

The area of the regular hexagon is equal to the area of six congruent equilateral triangles

Applying the law of sines to calculate the area of triangle

Remember that the measure of the interior angle in a equilateral triangle is 60 degrees

so

`A=6[(1)/(2) b^2sin(60^o)]`

`b=5.4\ in`

substitute

`A=6[(1)/(2) (5.4)^2sin(60^o)]=75.76\ in^2`

therefore

The area of each tile is about 76 square inches