Question

You are buying fabric to make a patio umbrella in the shape of a regular hexagon, as shown. The red fabric costs $3 per square yard and the white fabric costs $1.75 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?

Answer 1

Answer:

$14.25

Step-by-step explanation:

This is a hexagon. Therefore all the angles are  60º.

4ft = 4/3 yd

Area of one triangle

= √3/4 (4/3)²

= √3/4 (16/9)

= (4√3)/9 yd²

Area of 3 triangles

=  (4√3)/9 x 3

= (4√3)/3 yd²

= 3 yd² (Next whole number)

Cost of red fabric = 3 x 3 = $9

Cost of white fabric = 3 x 1.75 = $5.25

Total cost = 9 + 5.25 = $14.25

Answer 2

Given the fabrics has a shape of a regular hexagon, the cost of the fabric for the project will be: $14.25.

What is a Regular Hexagon?

A regular hexagon is a polygon that has 6 angles and 6 sides that are equal to each other.

Thus, since we are given a regular hexagon, it means each interior angle equals 60°.

Find the area of each colored triangle:

4 ft = 1.3 yd (3 ft = 1 yd)

Area = √3/4 × (1.3)² =  0.77 yd²

Therefore:

Area of the 3 triangles = 3 × 0.77 = 2.31 yd² (approximately, we would need 3 yd² of red fabrics and 3 yd² of white Fabrics).

Cost of red fabrics = $3 × 3yd² = $9.

Cost of white fabrics = $1.75 × 3yd² = $5.25

Total cost of fabrics = $9 + $5.25 = $14.25.

Learn more about regular hexagon on:

https://brainly.com/question/10209400