The area of a kite can be found, given the lengths of its diagonals
The correct option for the area of the kite ABCD is option C;
C) 162 square inches
The reason the selected value is correct is as follows:
The given parameters in the kite ABCD are;
AC = 18 inches
BE = 9 inches
The required parameter:
The area of the kite
Solution:
The area of a kite is given by the product of the lengths of the diagonals divided by 2
Therefore, we have;
[tex]\mathbf{The \ area \ of \ the \ kite \ ABCD} = \dfrac{Length (AC)\times Length (BD)}{2}[/tex]
The length of BD = BE + DE
BE = DE Given that AC is a perpendicular bisector of BD, by the properties of a kite
∴ BD = BE + BE = 2 × BE by substitution property
Therefore;
[tex]The \ area \ of \ the \ kite \ ABCD = \mathbf{\dfrac{Length (AC)\times 2 \times Length (BE)}{2} }= AC \times BE[/tex]
Which gives;
The area of the kite ABCD = 18 inches × 9 inches = 162 square inches
Learn more about the area of geometric shapes here:
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