Question

kite ABCD with angle A=60 degrees and angle C=90 degrees, diagonal DB=12 find the area and perimeter

Answer 1

In my diagram, angle C is at the top = 90°
then triangle BCD is an isosceles right-angled triangle with angle CBD = 45°
Let the diagonals intersect each other at E.
It is easy to see that EB = 6
then tan 45° = CE/6
CE = 6, (which we could have found by the isosceles triangle property)
by the 45-45-90 triangle ratios, BC = 6√2

look at triangel ABD, it is similar to the 30-60-90 triangle whose ratios of sides is 1 : √3 : 2
BA/2= 6/1 = AE/√3
AE = 6√3
AB = 12
perimeter = 6√2+6√2+12+12 = 24+12√2

area = (1/2)(12)(6) + (1/2)(12)(6√3) = 36 + 36√3

check my arithmetic