Answer:
Area of the given kite = 84 square inches.
Step-by-step explanation:
Properties of the diagonals of a kite,
1). Diagonals are perpendicular to each other.
2). Longer diagonal bisects the smaller one.
Therefore, Length of smaller diagonal BD = 2×6 = 12"
In right ΔAEB,
m∠ABE = m∠EAB = 45°
Therefore, in isosceles triangle AEB,
AE = BE = 6"
Now the length of longer diagonal AC = AE + EC
AC = 6" + 8"
= 14"
Area of the given kite ABCD = [tex]\frac{1}{2}(d_1)(d_2)[/tex]
= [tex]\frac{1}{2}(AC)(BD)[/tex]
= [tex]\frac{1}{2}(14)(12)[/tex]
= 84 square inches
