How do you get the area of a parallelogram and a square?

Question

Need to figure out what formula to use to get the are of a parallelogram with a square

Answer 1

The area of a square is simply the length of side squared.  That's because every side of a square is equal.  Remember that a square is a special case of a rectangle.  The area of a rectangle is the length times the width.

 

The area of a parallelogram is the base times the height.  Visualize a parallelogram as a rectangle sandwiched between two right triangles.  The area of the rectangle is the length times the width.  The area of each triangle is 1/2 the triangle base times the height.  So we have the total area as:

 

2(1/2 triangle base * height) + width of rectangle*height = height*(triangle base + width).

 

Now one triangle base + width is simply the base of the parallelogram.  So the area of a parallelogram is:

 

parallelogram area = parallelogram base * height

 

 ..........................

   .  |                    |.

     .| ^HEIGHT          |  .

      |...................|.....

               ^{WIDTH        TRIANGLE}

                                               ^BASE

Answer 2

Tera,

 

You should probably think of this problem as being in two parts.

 

The area of the square is easy. The area is the square's length times  its height (as long as the two are given in the same unit of measurement.

 

You should be left with two triangles.  The area of a triangle is one-half the length of its base times the length of its height.  But, since there are two triangles, the total area is twice that of either triangle by itself (assuming that the triangles are equal).