# Math Help - Designing a Rug With Ellipses and Circles

1. ## Designing a Rug With Ellipses and Circles

Louise uses an ellipse (see attachment) and two circles to design a rug. The diagram shows her design, drawn on a number plane.

a. Calculate the area of the shaded region.

How would I do so?

Note: The width of the ellipse is 5 and the radius of the small circle is 3.

Louise uses an ellipse (see attachment) and two circles to design a rug. The diagram shows her design, drawn on a number plane.

a. Calculate the area of the shaded region.

How would I do so?

Note: The width of the ellipse is 5 and the radius of the small circle is 3.
the width of the ellipse is 5 the radius is also 5.
area of ellipse = pi*a*b = pi*5*3
now we only have to deal with one half of the ellipse and larger circle.
so 0.5*pi*5*3
the area of the semicircle would be 0.5*pi*5^2
now area of semicircle minus area of half the ellipse and you get the area of the shaded region

3. Thank you for your above post. A good explanation makes Mathematics seem so much easier.

b. Louise is binding the circumference of the smaller circle with wool. She uses 80 g of wool for every metre. How many grams of wool will she use?

Correct me if I am wrong.

2*pi*3 = 18.85 m
18.85*80 = 1508 g

Therefore, she will use 1508 g of wool.

Thank you for your above post. A good explanation makes Mathematics seem so much easier.

b. Louise is binding the circumference of the larger circle with wool. She uses 80 g of wool for every metre. How many grams of wool will she use?

Correct me if I am wrong.

2*pi*3 = 18.85 m
18.85*80 = 1508 g

Therefore, she will use 1508 g of wool.
if she is binding the larger circle, it would be 2*pi*5 instead of 3, but you have the concept correct