The picture below shows the parallelogram formed by the intersection of two pairs of parallel lines?

What is the area of this parallelogram? And the perimeter?

Let ABCD is a parallelogram is formed by two set of parallel lines.

The distance between the two horizontal lines is 3 cm,

The distance between the vertically slanted lines is 2 cm.

Connect the two vertically slanted lines a right-angle triangle is formed.

From the right-angle triangle ABE

AB is the hypotenuse

AE is the opposite side

EB is the Adjacent side to θ

Sin θ = =

∴ θ = 30^o

∴ ∠ ABE is 30^o

From the fig. we can say that ∠ C = ∠ ABE = 30^o

In parallelogram opposite sides are equal

∴ ∠ BAD = ∠ C

∠ BAD = 30^o

∵ ∠ BAF = 90^o

∠ BAF = ∠ BAD + ∠ DAF

90^o = 30^o + ∠ DAF

∠ DAF = 60^o

From the diagram cos θ =

COS 60^o =

DA = 6 cm

We know that AD, AB are the sides of the parallelogram

Perimeter = 2 (AB + AD)

= 2 (4+6)

= 20 CM

Area = side × perpendicular distance to the opposite side

= AB × AF

= 4 × 3 = 12 cm²