Derive Area of Rectangle

[nycmathguy]

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

 

[MathLover1]

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

 

[nycmathguy]

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.

View attachment 3831

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

You definitely know mathematics. God blessed you with this skill. Lucky you.