Geometry Knowledge Is Required

Question

The link below is the picture of the parallelogram. I have been trying at this problem for a very long time. A detailed explanation would be helpful!

Find the area of the parallelogram pictured below. 

http://i64.tinypic.com/1tuau1.gif

Answer 1

The crux of this problem centers around two or three things you should know. The diagram shows that the sides of the parallelogram are 7 and 4 inches. By droping a line from upper left corner, you get a rt. triangle, and by finding the length of the vertical leg of the triangle, you can then use the formula length x width = Area. To find the vertical leg, you are going to apply the properties of the special right triangle--because you know the value of all of the angles--the right angle is 90, you are given the 60 degree angle, so the remaining angle must be 30. (Sum of the angles of a triangle are 180, and a right triangle always has an angle of 90 degrees). Plus, you know the length of the hypotenuse of that triangle, as that length has to be same as labeled side on the other side of the parallelogram (4 inches). Now you have the opportunity to choose one of the ratios of sine, cosine, and tangent to determine the length of the sides of the triangle.

(SOH-CAH-TOA) Choose an angle (I'd probably go with Sine of 60degree = Opposite/Hypotenuse

Sin 60 = x/4 in

Then substitute x in for the width, and 7 in for the length of the rectangle, and you are home free.

Hope this helps.

Meanwhile, you can find me at: https://www.wyzant.com/Tutors/gentle_tutor

I'd be happy to do this for you step by step in demo lesson.