4)
The picture below shows the parallelogram formed by the intersec-
tion of two pairs of parallel lines?
3 cm.
4 cm.
2 cm.
What is the area of this parallelogram? And the perimeter?
Answers
Answer:
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 = 30o
∴ ∠ ABE is 30o
From the fig. we can say that ∠ C = ∠ ABE = 30o
In parallelogram opposite sides are equal
∴ ∠ BAD = ∠ C
∠ BAD = 30o
∵ ∠ BAF = 90o
∠ BAF = ∠ BAD + ∠ DAF
90o = 30o + ∠ DAF
∠ DAF = 60o
From the diagram cos θ =
COS 60o =
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