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 A B C D 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 A B E . A B is the hypotenuse, A E is the opposite side, E B is the Adjacent side to θ . sin θ = Opposite Side Hypotenus = 2 4 ∴ θ = 30 ° ∴ ∠ A B E is 30 ° From the figure, we can say that ∠ C = ∠ A B E = 30 ° . In parallelogram opposite angles are equal. ∴ ∠ B A D = ∠ C ∠ B A D = 30 ° ∴ ∠ B A F = 90 ° ∠ B A F = ∠ B A D + ∠ D A F 90 ° = 30 ° + ∠ D A F ∠ D A F = 60 ° From the diagram cos θ = A F D A cos 60 ° = 3 DA D A = 6 cm We know that, A D , A B are the sides of the parallelogram. Perimeter = 2 ( A B + A D ) = 2 ( 4 + 6 ) = 20 cm Area of parallelogram = Side × Perpendicular distance to the opposite side = A B × A F = 4 × 3 = 12 cm 2

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Standard 8 Mathematics Part - 2>Chapter 3 - Area of Quadrilaterals>Exercise 1

Kerala Board Solutions for Chapter: Area of Quadrilaterals, Exercise 1: Exercise 1

Author:Kerala Board

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Area of Quadrilaterals, Exercise 1: Exercise 1

Attempt the free practice questions on Chapter 3: Area of Quadrilaterals, Exercise 1: Exercise 1 with hints and solutions to strengthen your understanding. Standard 8 Mathematics Part - 2 solutions are prepared by Experienced Embibe Experts.