Question

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?

Answer 1

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

Answer 2

Base of each parallelogram is
`3(2)/(4)yards`

The area of the smallest rectangle of wall that the mirror could fit on
`24(1)/(2) yards^(2)`

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 =
`(28)/(3) yards^(2)`

Since this is the area of two combined congruent parallelograms

So, area of each parallelogram =
`((28)/(3))/(2)=(14)/(3)`

Thus area of each parallelogram is
`(14)/(3) yards^(2)`

To Calculate base of each parallelogram

Formula of area of parallelogram = Base * Height

Since height of each parallelogram is
`1(1)/(3) =(4)/(3)`

Thus
`(14)/(3) = Base *=(4)/(3)`

`(14*3)/(3*4) = Base`

`(14)/(4) = Base`

`(7)/(2)yards = Base`

`3(1)/(2)yards = Base`

hence the base of each parallelogram is
`3(1)/(2)yards`

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

So, in this case length will increase since two parallelograms are combines so length of the resultant will be twice the length of each parallelogram

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 =
`24(1)/(2) yards^(2)`

The area of the smallest rectangle of wall that the mirror could fit on
`24(1)/(2) yards^(2)`