a We are given that Omar wants to make a replica of Guyana's national flag. To find the area of the piece of fabric he will need for the red and the yellow regions, let's take a look at the diagram.
First we can find the area of a red region, which is a triangle with a base of 2 feet and a height of 1 feet. Recall that the area of a triangle is the half of the product of its base and the corresponding height.
A_r=1/2( 2)( 1)=1
The area of the red region is 1 square feet. Now we can evaluate the area of the yellow region. Notice that this area will be the difference between the area of a triangle that contains the red and yellow regions, and the area of the red triangle.
A_y=A_(r+y)-A_r=1/2( 2)( 2)-1=1
The area of the yellow region is also 1 square foot.
b In this part we are asked to find the cost of the fabric if one square yard of each color costs $3.99. First we should evaluate the area of the whole flag, which is a rectangle.
Recall that the area of a rectangle is the product of its length — which is 2 feet — and its width, which is also 2 feet.
A= 2* 2=4
The area of the whole flag is 4 square feet. To determine how much we will pay for the paint we need to convert square feet to square yards. Recall that there are 3 feet in each yard, so each square yard is equivalent to 3^2=9 square feet. Using this fact, we can convert square feet to square yards.
4ft^2=4ft^2* 1yd^2/9ft^2=4/9yd^2
Finally we will multiply this area by $3.99.
4/9*$3.99≈ $1.77
It will cost approximately $1.77 to make the whole flag.
