Asked by Kathy
kite ABCD with angle A=60 degrees and angle C=90 degrees, diagonal DB=12 find the area and perimeter
Answers
Answered by
Reiny
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.