Question

PLEASE HELP WILL AWARD BRAINLIEST TO BEST ANSWER!!!

Answer 1

Answer:

See below

Step-by-step explanation:

$In\: \triangle AKL, \:\\ AK = 9,\: \\m\angle K = 90\degree, \: \\m\angle A= 60\degree \\\therefore m\angle L = 30\degree\\By \:30°-60°-90° \:\triangle \:theorem:\\AK = \frac{1}{2} \times AL\\(SIDE\: OPPOSITE \:TO \:30\degree) \\\\9 = \frac{1}{2} \times AL\\\\AL = 9\times 2\\\\\huge\red{AL = 18}\\\\KL = \frac{\sqrt 3}{2} \times AL\\(SIDE\: OPPOSITE \:TO \:60\degree) \\\\KL = \frac{\sqrt 3}{2}\times 18\\\\KL = 9\times \sqrt 3\\\\\huge\purple{KL = 9\sqrt 3}\\\\P(\triangle AKL) = AK + KL + AL\\P(\triangle AKL)= 9 + 9\sqrt 3+18\\\huge\orange{P(\triangle AKL)=(27 + 9\sqrt 3) \: units} \\\\A(\triangle AKL) = \frac{1}{2} \times KL\times AK\\A(\triangle AKL) = \frac{1}{2} \times 9\sqrt 3\times 9\\A(\triangle AKL) = \frac{81\sqrt 3}{2} \\\huge\pink{A(\triangle AKL) = 40.5\sqrt 3\: units^2}$