Respuesta :

roohafzah

Answer :

  • 128√3

Explanation :

The area of a rhombus is given by,

  • (diagonl 1*diagonal 2)/2

also, we should remember that the diagonals of a rhombus bisect each other at 90° thus,

  • diagonl 1 = 2*8 = 16
  • diagonl 2 = ?

we can find the diagonal 2 by finding the measure of one of the bisected part of the diagonal using the law of sines .Let it be x then,

  • sinA/a = sinB/b

here,

  • A = 60°
  • a = x
  • B = 30 [ 180° - (90° + 60° ) ]
  • b = 8

plugging in,

  • a = sinA*b/sinB
  • a = sin(60)*8/sin(30)
  • a = 8√3

thus, the measure of diagonl 2 would be equal to

  • 8√3*2
  • 16√3

therefore,the area of the rhombus would be

  • area = (16*16√3)/2
  • area = 128√3

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