Answer:
Option A is correct i.e Area is 56 square centimeter.
Step-by-step explanation:
Given EC = 10cm, AE = 4cm, and m∠EAB = 45°. we have to find the area of kite.
In ΔABE, ∠EAB = 45°
[tex]tan\angle EAB=\frac{BE}{AE}[/tex]
⇒ [tex]tan 45^{\circ}=\frac{BE}{4}[/tex]
⇒ BE=4 cm
BE=ED=4 cm (one diagonal of kite bisect other)
BD=BE+ED=4+4=8 cm
AC=AE+EC=4+10=14 cm
[tex]\text{Area of kite=}\frac{pq}{2}[/tex], where p and q are the diagonals
⇒ [tex]\text{Area of kite ABCD=}\frac{8\times 14}{2}=56cm^2[/tex]
Option A is correct.
