A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 squar

Given:
Two identical parallelograms total area = 9 1/3 yd²
Each parallelogram has height 1 1/3 yd

Area formula: area = base × height

Split the total area equally to find each parallelogram's area.

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

Divide by 2: 28/3 × 1/2 = 28/6 yd², which is 4 4/6 yd² → 4 2/3 yd²

So each parallelogram's area is 4 2/3 yd²

Set up base × 1 1/3 yd = 4 2/3 yd²

Convert and divide: 14/3 yd² ÷ 4/3 yd = base

Multiply: 14/3 × 3/4 = base
Compute: 14*3 / 3*4 = base
42 / 12 = base
Which simplifies to 3 6/12 yd = base
or 3 1/2 yd = base

a) Each parallelogram has a base of 3 1/2 yards
b) If the two parallelograms form a rectangle:
Rectangle area = length × width

Length = 3 1/2 yd × 2 = 7 yds
Width = 3 1/2 yds

Area = 7 yd × 3 1/2 yd
Area = 7 × 7/2 yd²
Area = 7*7 / 2 yd²
Area = 49 / 2 yd²
Area = 24 1/2 yd²

Answer:

Base of each parallelogram is  

The area of the smallest rectangle of wall that the mirror could fit on  

Step-by-step explanation:

Given: The parallelograms have a combined area of 9 1/3 square yards. The height of each parallelogram is 1 1/3 yards.

To Find: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?

Solution:

Since The parallelograms have a combined area of 9 1/3 square yards =

Because these are two congruent parallelograms combined,

the area for each is half the total

So each parallelogram's area is

To find the base of each parallelogram

Use area = Base * Height

Given the height is

Thus  

hence the base of each parallelogram is  

b) assume the two parallelograms form a rectangle.

So the overall length doubles the individual base

area of a rectangle is length times width.

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

width is 3 1/2 yards

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

Area = 7 yd * 7/2 yd

Area = 7*7 / 2 yd²

Area = 49 / 2 yd²

Area =

The area of the smallest rectangle of wall that the mirror could fit on