a 24in^2 each of yellow, red, orange, green, and blue; 20in^2 of purple
B
b Yes, see solution.
Practice makes perfect
a We are given that Ashanti is in the kite competition, and her kite is made of five congruent rhombi that have different colors and one purple kite. Let's take a look at the diagram. All of the given dimensions are in inches.
Recall that both a rhombus and a kite have the same formula for the area. In this formula d_1 and d_2 are diagonals.
A=1/2d_1d_2
Using this formula we can evaluate the area of rhombi and the kite to determine how much fabric of each color Ashanti needs. Let's start with a yellow rhombus.
As we can see one diagonal has a length of 3+ 3=6 inches and the second one is 4+ 4=8 inches. Let's substitute these values into area formula.
The area of each piece that is a rhombus is 24 square inches. Therefore Ashanti needs 24 square inches of yellow, red, orange, green and blue fabrics. Now we will evaluate the area of the purple kite.
In this figure one diagonal has a length of 2+ 3=5 inches and the other has a length of 4+ 4=8 inches. By using these we will find the area of this kite.
The area of the kite is 20 square inches. This means that Ashanti needs 20 squares inches of purple fabric.
b In this part we are given that competition rules requires that the total area of each kite be no greater than 200 square inches. To determine whether Ashanti's kite meet this requirement we need to find its total area. To do this we will use the areas of each piece that we found in the previous part.
Let's add the area of the purple kite, 20 in^2, and the areas of five rhombi, 24 in^2 each.
20+5*24=140
Ashanti's kite has the area of 140 square inches, which is less than 200 in^2. Therefore her kite meets the requirement.
