Derive the formula A = (width)(length).

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. 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