A parallelogram is a regular polygon with four sides and vertices. It is a quadrilateral formed by two pairs of parallel lines. A parallelogram with right angles is known as a rectangle. We will discuss how to prove that the Area of a Parallelogram is Equal to that of a Rectangle Between the Same Parallel Lines.
Area of a Parallelogram is Equal to that of a Rectangle Between the Same Parallel Lines – Theorem
Prove that Area of the parallelogram is equal to that of the rectangle on the same base and of the same height that is between the same parallel lines.
Proof:
PS = QR [opposite sides of the parallelogram PQRS]
PN = QM [Opposite sides of the rectangle PQMN]
∠PNS = ∠QMR [Noth are right angles, PQMN being a rectangle]
∆PNS ≅ ∆QMR
ar(∆PNS) = ar(∆QMR)
ar(∆PNS) + ar(Quadrilateral PQMS) = ar(∆QMR) + ar(Quadrilateral PQMS)
We know that the rectangle and parallelogram are on the same base and between the same parallel lines and the height of the parallel line at every point is constant.
Let b be the base of the rectangle
Let h be the height of the line is h
The height of the parallel line is nothing but the breadth of the rectangle.
Area of the rectangle = length × breadth
Also, we can write it as base × height
The area of the parallelogram is base × height
Therefore, area of a rectangle = Area of the parallelogram
Hence Proved.
See More: A Parallelogram, whose Diagonals are of Equal Length, is a Rectangle
FAQs on Area of a Parallelogram is Equal to that of a Rectangle Between the Same Parallel Lines
1. What is the relation between the area of parallelogram and rectangle standing on the same base and between the same parallels?
Parallelograms and rectangles on the same base and between the same parallels are equal in area.
2. Are parallel lines equal in a parallelogram?
A quadrilateral with two pairs of parallel lines is known as a parallelogram. The opposite sides of a parallelogram are always equal in length and parallel.
3. Is a parallelogram a rectangle True or false?
Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. A parallelogram is a rectangle.