A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 square yards. The height of each parallelogram is 1 1/3 yards. a) how long is the base of each parallelogram? b) what is the area of the smallest rectangle of wall that the mirror could fit on?

Given:

2 parallelograms with an area of 9 1/3 yd²

height of each parallelogram is 1 1/3 yd

Area of parallelogram = base * height

We need to divide the combined area into two to get each parallelogram's base.

9 1/3 = ((9*3) + 1) / 3 = 28/3

28/3 : 2 = 28/3 * 1/2 = 28/6 yd² or 4 4/6 yd² ⇒ 4 2/3 yd²

Area of each parallelogram is 4 2/3 yd²

4 2/3 yd² = base * 1 1/3 yd

14/3 yd² : 4/3 yd = base

14/3 yd² x 3/4 yd = base

14*3 / 3*4 = base

42 / 12 = base

3 6/12 yd = base

or 3 1/2 yd = base

a) the base of each parallelogram is 3 1/2 yards

b) we can assume that the two parallelograms form a rectangle.

area of a rectangle is length times width.

length is 3 1/2 yds * 2 = 7 yds

width is 3 1/2 yds

Area of rectangle = 7 yds * 3 1/2 yds

Area = 7 yd * 7/2 yd

Area = 7*7 / 2 yd²

Area = 49 / 2 yd²

Area = 24 1/2 yd²