Question

Using the design below, you plan to make a rectangular wall hanging to decorate yourbedroom. Th e green rectangle is 16 ft by 10 ft, the blue square is 7 ft by 7 ft, the orangetriangles have a height of 1.73 ft and a side length of 2 ft, and the yellow circle has adiameter of 3 ft. You plan to glue the pieces together and then outline each piece withblack cord.a. How much black cord does the design use?b. How much fabric of each color does the design show?c. At a craft store, fabric comes in bolts that are a fixed number of inches wide.You can only buy fabric by the whole yard. If each bolt is 48 in. wide, what isthe least amount of each color that you need to buy? Explain.please I try to solve it but I did not understand it please need help thank you so much.

Answer 1

To know the total amount of fabric we need per color, we need to find the area of each color.

The green rectangle.

$A_{green}=16\cdot10=160ft^2$

The blue square.

$A_{blue}=7\cdot7=49ft^2$

The orange triangles.

$A_{orange}=4(\frac{1}{2}\cdot1.75\cdot2)=\frac{14}{2}=7ft^2$

The yellow circle.

$A_{circle}=\pi r^2=3.14\cdot(1.5)^2=3.14\cdot2.25=7.065ft^2$

Now, the bolts are sold in fixed yards, we know that 48 inches are equivalent to 1.333... yards, or 4 feet. But, we are using areas so, 48 to the square power in square inches would be equivalent to 16 square feet.

Then, we divide each area by 16 square feet.

$b_{green}=\frac{160}{16}=10$

We need 10 bolts of green fabric.

$b_{blue}=\frac{49}{16}=3.0625$

We need 4 bolts of fabric since if we use 3 we would need a bit more.

$b_{orange}=\frac{7}{16}=0.4375$

We just need 1 bolt of orange fabric.

$b_{yellow}=\frac{7.065}{16}=0.44$

We need 1 bolt of yellow.