SOLUTION: A parallelogram with a perimeter of 20 yards has a height of 3 yrds. Tammy does not know how many yards the base is, but se does know that the side adjoining the base is 4 yrds. Wh

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Question 271760: A parallelogram with a perimeter of 20 yards has a height of 3 yrds. Tammy does not know how many yards the base is, but se does know that the side adjoining the base is 4 yrds. What is the area of the parallelogram?
I know the answer is to be 18yds, but I do not know whow to get it to explane to my 11 year old son.
Found 2 solutions by Theo, scott8148:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
perimeter of the parallelogram is 20 yards.
the height of the parallelogram is 3 yards.

the area of the parallelogram is height * base.

the perimeter of the parallelogram is 20 yards.

the side adjoining the base is 4 yards.

in a parallelogram, the opposite sides are both parallel to each other and equal to each other.

this means that 2 times the base of the parallelogram plus 2 times the adjoining side of the parallelogram equals the perimeter of the parallelogram.

2 times the adjoining side = 8.

8 subtracted from 20 = 12

12/2 = 6

the base of the parallelogram is 6 yards long.

the area of the parallelogram is the height times the base = 3 * 6 = 18 square yards.

here's your parallelogram: 
                                 6 yards
                                    |
                         x x x x x x x x x x
                        x            x    x
        4 yards --     x             x   x
                      x 3 yards --   x  x   -- 4 yards
                     x               x x
                    x x x x x x x x x x 
                           |
                        6 yards

the base and the side opposite it are each equal to 6 yards in length.
the right side and the side opposite to it are each equal to 4 yards in length.
the altitude is equal to 3 yards in length.









Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the opposite sides of a parallelogram are parallel AND equal

"the side adjoining the base is 4 yrds" ___ so the opposite side is also 4 yds
___ the two sides sum to 8 yds (4 + 4)
___ this leaves 12 yds (20 - 8) for the other two sides ___ they are 6 yds (12 / 2) each

so the base of the parallelogram is 6 yds and the height is given as 3 yds
___ area is base times height or 18 yd^2