On asking a child “What is area?”, he/she answered length × breadth. What can you say about the child’s understanding about the concept of area?

Correct Answer: The child used the area of rectangle as general idea of area of any closed shape.

Step-by-Step Explanation:

1. Understanding the Concept of Area:
Area is defined as the measure of the total space or region enclosed within a two-dimensional closed boundary or shape. Different geometrical shapes (such as triangles, circles, trapezoids, and rectangles) have different mathematical formulas to calculate their area depending on their specific properties and dimensions.

2. Analyzing the Child's Response:
When asked "What is area?", the child responded with "$\text{length}\times \text{breadth}$".
The formula $\text{length}\times \text{breadth}$ specifically applies to calculating the area of a rectangle (or a square, which is a special type of rectangle). It is not the general definition of area for all closed shapes.

3. Evaluating the Child's Misconception:
The child's answer shows that while they know how to compute the area of one specific shape (a rectangle), they have generalized this specific formula as the universal definition for the concept of area as a whole. Therefore, the child is using the area of a rectangle as a general idea for the area of any closed shape.