You are buying fabric to make a patio umbrella in the shape of a regular hexagon, as shown. The blue fabric costs $3.50 per square yard and the white fabric costs $2 per
square yard. You can only order whole numbers of square yards of fabric. What will be the cost of the fabric for this project?
5 ft
3

cost of the fabric = $22

Step-by-step explanation:

The picture is a regular hexagonal which means it has six sides of equal length. The triangle in the hexagons are equilateral triangle. This means they have equal length. The blue portion is just like half the area of the hexagon while the white part is also half the area . Note both colors cover 3 triangle each.

area of the hexagon = 3/2 × √3 × a²

where

a = sides

area of the hexagon = 3/2 × √3 × a²

a = 5 ft

convert ft to yard

3 ft = 1 yard

5 ft = 5/3 = 1.6666666667 yards

area = 3/2 × √3 × 1.6666666667²

area of the hexagon = 7.21687836516 yard²

Half of the area is the blue section area because 3 triangle makes half of the hexagon = 7.21687836516/2 = 3.60843918258  yard². Note we can only order whole number of square fabric . Therefore, 3.60843918258 ≈ 4

blue fabric cost $3.50 per square yard.

The cost for this yard = 4  × 3.50 = $14  

white fabric cost $2 per square yard .

The cost for this yard = 4  × 2 = $8

Total cost = 14  + 8  = $22

cost of the fabric = $22

29.5977692753

step-by-step explanation: