Question

a greeting card uses a geometric design containing 4 congruent kites. the card is 4 inches wide and 8 inches long. what is the area of one kite? 4 sq. in. 8 sq. in. 12 sq. in. 16 sq. in.

Explanation:

Step1: Calculate the area of the rectangle

The area formula of a rectangle is \(A = length\times width\). Given \(length = 8\) inches and \(width = 4\) inches. So, \(A_{rectangle}=8\times4 = 32\) square inches.

Step2: Analyze the relationship between the rectangle and the kites

Since there are 4 congruent kites in the rectangle. Let the area of one kite be \(A_{kite}\). Then \(A_{rectangle}=4\times A_{kite}\).

Step3: Solve for the area of one kite

From \(A_{rectangle}=4\times A_{kite}\), we can get \(A_{kite}=\frac{A_{rectangle}}{4}\). Substitute \(A_{rectangle} = 32\) into the formula, \(A_{kite}=\frac{32}{4}=8\) square inches.

Answer:

8 sq. in.