Let two rectangles which are shown here:

Here A is a rectangle, and diagonal is cutting this rectangle in two equal halves. Both the triangles are congruent. Hence their area will be equal.

Therefore,

Area of rectangle = Area of one triangle + Area of another triangle

⇒Area of rectangle = 2 `xx` Area of one triangle (As both the triangles are equal)

`2 xx 1/2 xx` length `xx` breadth

= length `xx` breadth

Similarly, For figure B, which is a square and diagonals cut that in four equal triangles. Means all triangles are congruent.

Area of square = 2 `xx` Area of triangle

`= 2 xx 1/2 xx` Side^{2}

= Side^{2}

Let us consider the rectangle given in the figure. In this a Line EF is dividing the rectangle in two equal part. Both parts are congruent.

Hence, area of one part = area of other part.

Hence, area of each congruent part = Area of rectangle ÷ 2

**Question 1:** Each of the following rectangles of length 6 cm and breadth 4 cm is composed of congruent polygons. Find the area of each polygon.

**Solution:** Figure A has 6 congruent polygons.

Hence, area of each polygon = Area of rectangle ÷ 6

Area of rectangle = length X breadth

`= 6 xx 4 = 24` sq cm

Hence, area of each polygon of A `= 24 ÷ 6 = 4` cm^{2}

**Figure B has 4 congruent polygons.**

Hence, area of each polygon = Area of rectangle ÷ 4

`= 24 ÷ 4 = 6` sq cm

**Figure C has 2 congruent polygons.**

Hence, are of each polygon = Area of rectangle ÷ 2

`= 24 ÷ 2 = 12` sq cm

**Figure D has 2 congruent polygons.**

Hence, are of each polygon = Area of rectangle ÷ 2

`= 24 ÷ 2 = 12` sq cm

**Figure E has 8 congruent polygons.**

Hence, area of each polygon = Area of rectangle ÷ 8

`= 24 ÷ 8 = 3` sq cm

A polygon is said to be a parallelogram when their opposite sides are parallel.

Here; let ABCD is a parallelogram. In this AB is parallel to CD and AC is parallel to BD. One side BD of this parallelogram is extended and a perpendicular CE is drawn on it.

Here CE is called the Height of the parallelogram.

Hence;

Area of parallelogram ABCD = base x height

⇒ Area of a parallelogram = base x height.

**Question 2:** Find the area of following parallelograms:

(i) Given, Base = 8cm, Height = 3.5 cm

Therefore, Area = Base x Height

`= 8 xx 3.5c = 28.0` cm^{2}

(ii) Given, Base = 8cm, Height = 2.5 cm

Therefore, Area = Base `xx` Height

`= 8xx 2.5= 20.0` cm^{2}

(iii) In a parallelogram ABCD, AB = 7.2cm and the perpendicular from C on AB is 4.5cm.

Area of parallelogram ABCD = Base `xx` Height

`= 7.2 xx 4.5 = 32.40` cm^{2}

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