LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

AREA OF PARALLELOGRAM

__Area of Parallelogram__ –

**Let, PQRS be a parallelogram. Let us draw the
rectangle XQRY on the same base and between the same parallels as the
parallelogram PQRS. **

**Then, the area of the
parallelogram PQRS **

**= the area of a rectangle XQRY**** **

**= QR X RY = base X height**

**We can take any of the sides
as the base and multiply it by the corresponding height. For example, if we
take QR as a base, the corresponding height will be PY.**

**The area of a parallelogram
= base X height**

**Also, since each diagonal of a
parallelogram divides it into two congruent triangle**

**The area of parallelogram PQRS
**

**= 2 X area of (∆ PQR) = 2 X area of (∆ SPR)**

**Example.) A parallelogram has adjacent sides of 30 cm and 40
cm. if the distance between the longer sides in 20 cm, find (a) the area of the parallelogram and (b) the
distance between the shorter sides.**

**Let, WXYZ be the parallelogram.**

**Here, XY = WZ = 40 cm, ****XW = YZ = 20 cm, and distance between XY and WZ, that is AW = 10 cm**

**(a) area of the parallelogram = base
(XY) X height (AW) **

** = 40cm X 10cm = 400
cm² **

**(b) let AW, the distance between the
shorter sides XW & YZ = a cm**

**Then the area of parallelogram = base
(YZ) X height (BW) **

** 400 cm² = 20 cm X a**

** Or, a = 400 cm²/ 20 cm = 20 cm
(Ans.)**