Amirror 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?

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 =

Since this is the area of two combined congruent parallelograms

So, area of each parallelogram =

Thus area of each parallelogram is

To Calculate base of each parallelogram

Formula of area of parallelogram = Base * Height

Since height of each parallelogram is

Thus  

hence the base of each parallelogram is  

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 =

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

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )