Find the Area of a Large Rectangle

The problem of the unknown area

The problem is related to a large rectangle whose area is unknown. The rectangle is comprised of many small and large size squares and rectangles of different length, closed in it. The only available information is given in the form of a black square inside the rectangle, with unit length.

Finding the parameters of a rectangle or square

To find the area of a rectangle or square, it is essential to find the parameters like width and length. In a square, all the sides are equal. It means the width and the length will be the same. But in the rectangle, you have to find both the parameters. In the given problem, the black square has a unit length on each side, so we can find the area. The area of the black square and its connected side will assist in finding the parameters of other squares and rectangles. Then we will find all the areas inside respectively. Thus, adding all the squares will give the actual area of the large rectangle.

Application of the problem in construction

This problem is similar to houses and buildings construction where the size is in either square or rectangular form. Furthermore, the inside area is utilized to make rooms or partitions on the same basis, square or rectangle. That's why this problem is an advanced one due to its wide applications.

The importance of equations

In the problem, the representation is in diagram form. In mathematics, the equation is the most important factor which will lead you towards the solution. Therefore, we will use the formula or equation, Area = Length x Width. The equation can be used for both purposes, finding and verifying. You can further express the findings in any representational form like graphs, tables, words or diagrams.