Question

How do the areas of the parallelograms compare?

Answer 1

check the picture below.

get the area of each, compare them away.

notice though, regardless of the slantness, the height and base are the same length.

Answer 2

The statement that compares the area of two parallelograms is:

• The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

Explanation:

We know that the area of parallelogram is given by:

`Area=bh`

where b is the base of the parallelogram and h is the height of the parallelogram.

Parallelogram ABCD

Base(b)=AB

and Height(h)=DE

we have the coordinates of A,B,C,D and E as:

A(4,2) B(7,2) C(4,6) D(1,6) E(1,2)

Hence,

`AB=√((7-4)^2+(2-2)^2)\\\\\\AB=√(3^2)\\\\\\AB=3\ units`

`DE=√((1-1)^2+(2-6 )^2)\\\\\\DE=√(4^2)\\\\\\DE=4\ units`

Hence, Area of parallelogram ABCD= 3×4=12 square units

Similarly,

In Parallelogram EFGH

we have:

Base(b)=EF

Height(h)=GI

The coordinates are:

E(-2,2) F(-5,2) G(-6,6) H(-3,6) and I(-6,2)

Hence,

`EF=√((-5-(-2))^2+(2-2)^2)\\\\\\EF=√((-5+2)^2)\\\\\\EF=√((-3)^2)\\\\\\EF=√(3^2)\\\\\\EF=3\ units`

and

`GI=√((-6-(-6))^2+(2-6)^2)\\\\\\GI=√((-6+6)^2+(-4)^2)\\\\\\GI=√(4^2)\\\\\\GI=4\ units`

Hence,

Area of parallelogram EFGH= 3×4=12 square units