Question

Prove that area of rectangle
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Answer 1

Area of a Rectangle A = l × b

Answer 2

Answer:

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.

Area of Rectangle using Length and Breadth

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 x height = ½ x AB x BC = ½ x b x l

Area of ∆ADC = ½ x base x height = ½ x CD x AD = ½ x b x l

Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC

Area (ABCD) = 2(½ x b x l)

Area (ABCD) = l x b

Thus, the area of the rectangle = Length x Breadth