Part of a tiling design is shown. The center is a regular hexagon. A square is on each side of the hexagon, and an equilateral triangle joins the squares. Complete the pattern around the hexagon and calculate the total area of the pattern.

Question

Vocaloid · Answer

@terrshields01 is there a picture that goes with this?

terrshields01 · Answer

attachment

Vocaloid · Answer

first step would be to continue the pattern

Vocaloid · Answer

|dw:1507577584365:dw|

Vocaloid · Answer

each of the 6 squares' areas can be found with area = s^2

Vocaloid · Answer

the hexagon is made of 6 equilateral triangles with side 8

the formula for area for an equilateral triangle is sqrt(3)/4 s^2     let me know if you want me to derive this

Vocaloid · Answer

for the exterior triangles we need to do a bit of work

Vocaloid · Answer

|dw:1507577842180:dw|

Vocaloid · Answer

|dw:1507577849007:dw|

Vocaloid · Answer

120 + 90 + 90 + triangle angle  = 360

the angle inside the triangle is 60

Vocaloid · Answer

|dw:1507577918514:dw|

Vocaloid · Answer

since the exterior triangle is isosceles, the other two angles must also be 60 (180-60)/2 = 60

Vocaloid · Answer

meaning that the 6 exterior triangles are also equivalent to the interior triangles

Vocaloid · Answer

so, to recap, find the area of the hexagon, squares, and exterior triangles using the information I have given you

1 attachment