Question

Observe the picture of a hall. It has been divided by a line. One part of the hall is a stage of length x and breadth y. The remaining area of the hall is a square. What is the total area of the hall?

• A. $$x^2+y^2+2xy$$
• B. $$x^2+y^2$$
• C. $$x^2+xy$$
• D. $$x^2+2xy$$

Answer 1

Answer:

$$x^2+xy$$

Area Calculation of a Rectangular Hall with a Square Section

• The problem describes a hall that is divided into two parts: a rectangular stage and a remaining square area.

• The stage has dimensions of length 'x' and breadth 'y'. The area of this rectangular stage is calculated as: Area of Stage = length × breadth = x × y = xy.

• The remaining part of the hall is a square. From the provided image, it can be inferred that the side length of this square is equal to the breadth of the stage, which is 'y'.

• Therefore, the side of the square is 'y'. The area of this square section is calculated as: Area of Square = side × side = y × y = y².

• The total area of the hall is the sum of the area of the stage and the area of the square section.

• Total Area = Area of Stage + Area of Square = xy + y².