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.
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
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
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.
Area of parallelogram ABCD = base × height
⇒ Area of a parallelogram = base × height.
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