# Perimeter and Area

#### Triangles as Parts of Rectangles

Let us take 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 × 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 Side2

= Side2

##### Generalising for other Congruent Parts of Rectangles

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

### AREA OF A PARALLELOGRAM

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 × height

⇒ Area of a parallelogram = base × height.