Question

a kite is inscribed in a square with a side length of 9 units. what is the area of the kite? 36.0 square units 40.5 square units 45.0 square units 27.5 square units

Explanation:

Step1: Calculate the area of the square

The area formula of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 9\) units, then \(A_{square}=9\times9 = 81\) square units.

Step2: Analyze the relationship between the kite and the square

The kite divides the square into 8 congruent right - angled triangles. The kite is composed of 4 of these triangles. So the area of the kite is half of the area of the square.

Step3: Calculate the area of the kite

\(A_{kite}=\frac{1}{2}\times A_{square}\). Substitute \(A_{square}=81\) into the formula, we get \(A_{kite}=\frac{1}{2}\times81 = 40.5\) square units.

Answer:

40.5 square units