How would I find the area of this rectangle?

Question

I'm sorry, I know I just asked another math question, which I did figure out by the way, and I'm not trying to get others to do my work...this isn't even homework I just want to know how to do them for extra practice. The diagonals of a rectangle are 18 cm. long and intersect at a 60 degree angle. What is the area of the rectangle?

Answer 1

tthe ans is eighty one root three
81*3^0.5

consider the rectangle to be four triangles
each's area is 1\2*9*9*sin60

4<1/2*9*9*sin60>
81*square root of three

Answer 2

Well, there are probably a few ways to do it, but the way I would do it is this.

The diagonals will bisect each other at the very center of the rectangle. Take one of the resulting triangles with the 60 degree angle. You will have to divide this triangle in half so that you have a right triangle with a hypotenuse of 9 cm, two legs of half of the rectangles side lengths and a 30 degree angle. Using trig functions you can find the lengths of the sides of this triangle.

(9 cm)*cos(30) = 7.79423 cm
(9 cm)*sin(30) = 4.5 cm

As stated before, the legs of this triangle are half of the sides of the rectangle, therefore the sides of your rectangel are 9 cm and 15.5885 cm.

Then its simple.

9*15.5885 = 140.296 cm^2