The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.
Suppose, ABCD is a rectangle.
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Now, let diagonal AC divide the rectangle into two right triangles, i.e. ∆ABC and ∆ADC.
We know that ∆ABC and ∆ADC are congruent triangles.
Area of ∆ABC = ½ x base * height = ½ x AB *BC = ½ * b x w
Area of ∆ADC = ½ *base * height = ½ x CD * AD = ½ *b * w
Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC
Area (ABCD) = 2(½ *b * w)
Area (ABCD) = l x w
Thus, the area of the rectangle = Length x Width
