Question

HELP QUICK! Thank you!!!!!!!!

Answer 1

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