if the sides of parallelogram and an included angle are 8m 12m and 120degree respectively.Find the length of the shorter diagonal

Question

What is the area of the parallelogram

Answer 1

Hi Ken, we can find the length of the shorter diagonal using the formula:

 

Length of shorter diagonal = √(long side squared + short side squared - 2 * long side * short side * cos Θ)

 

Where:

Long side         = 12 meters

Short side        = 8 meters

Included angle = 120 degrees

 

Each pair of angles in the parallelogram equals 180 degrees. Since we want the shorter diagonal, we need to subtract 120 from 180 getting 60 degrees, or Θ = 60 degrees. 

 

Length of diagonal = √(12² + 8² - 2 * 12 * 8 * cos 60)

 

Length of the shorter diagonal = 10.58 m

 

Questions?