Question

Find the area of the kite with the given information.​

Answer 1

Area of the given kite = 84 square inches.

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 =
`(1)/(2)(d_1)(d_2)`

=
`(1)/(2)(AC)(BD)`

=
`(1)/(2)(14)(12)`

= 84 square inches