Find the area of each parallelogram. what is the relationship between the areas?

Area of parallelogram is given by:

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

In parallelogram TQRS.

Coordinate of TQRS are;

T(8, 16), Q(4, 4), R(16, 4) and S(20, 16)

Coordinate of T'Q'R'S' are;

T'(2, 4), Q'(1, 1), R'(4, 1) and S'(5, 4)

Find the length of QR and PT:

Using distance(D) formula:

units

Similarly;

For PT:

From the graph:

P(8, 4) and T(8, 16), then

units

In parallelogram TQRS

PT represents the height and QR represents the base of the parallelogram respectively.

then;

Area of parallelogram TQRS =

⇒Area of parallelogram TQRS = unit square.

Now, in parallelogram T'Q'R'S'

Q'R' represents the base and P'T' represents the height of the parallelogram respectively.

here, P'(2, 1)

Find the length of Q'R' and P'T':

units

units

Then;

Area of parallelogram T'Q'R'S' =

Area of parallelogram T'Q'R'S' = unit square.

Now, we have to find the relationship between the areas.

then;

the relationship between the areas of TQRS and T'Q'R'S' is: