Question

Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.

A: 72√3 sq. units
B: 36√3 sq. units
C: 12√3 sq. units

Answer 1

I think I got it. Correct me if I am wrong.

Parallelogram diagram I believe down below. We must find the height and then the area using Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.

A^2 + B^2 = C^2
A^2 + 3^2 = 6^2
    A^2 + 9 = 36
          A^2 = 27
              A = 3√3

Therefore the height is 3√3

Now calculate the area using A = bh

A = bh
   = (12)(3√3)
   = 36√3

So the area is 36√3 square units.

I cannot be sure of this answer because you did not provide a diagram.

Answer 2

The area of the parallelogram will be equal to 36√3 square units.

What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.

Parallelogram diagram I believe down below. We must find the height and then the area using the Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.

A ² +   B²  =  C²

A²  +   3²   =  6²

A²  +   9    = 36

A²   =    27

A = 3√3

Therefore the height is 3√3. Now calculate the area using A = bh

A   =  b   x   h

A   =  ( 12 )   x   ( 3√3 )

A   =  36√3

So the area is 36√3 square units.

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