Two sides of a parallelogram are 14 feet and 15 feet.

Question

Two sides of a parallelogram are 14 feet and 15 feet. The measure of the angle between these sides is 95°. Find the area of the parallelogram to the nearest square foot.

Answer 1

It is the exact same process as any of the last questions you have asked

Answer 2

Hi Ray,

 

Lets say that parallelogram ABCD with angle A in the lower left hand corner and angle B in the lower right hand corner. If ∠B = 95 then ∠A = 85. Angle D is in the upper left hand corner of the parallelogram. Draw an altitude from D to AB. This forms a right triangle ADE where AD is the side opposite ∠A. Let the side AD measure 15 and side AB measure 14. Name the altitude x. The area of a parallelogram is the base times the altitude. To find the altitude use the sin ratio.

             sin 85 = x/15 and solve for x   to get  x = 15 sin 85 = 14.94292047.  Now the area is

 

                  A = (1/2)(14)(14.94292047) = 104.6 or   105 square feet.  Note:If you use a calculator to find the altitude, do not round this calculation, but keep it in your calculator and multiply by (1/2)(14).