Perimeter and Area

Triangles as Parts of Rectangles

Let us take two rectangles which are shown here:

rectangle square

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.

rectangle

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.

parallelogram

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.



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