Question

lini says the rectangle is divided into four parts with equal areas. david says the four parts do not have equal areas. who is correct? explain your answer.

Explanation:

Step1: Analyze area - division concept

Equal - area division means each part has the same amount of space within the rectangle. Just because the shapes of the parts are different does not mean the areas are unequal.

Step2: Consider area formula for rectangle parts

If we can show that the parts can be calculated to have the same area value (for example, by splitting the rectangle into sub - rectangles or using other geometric area formulas), we can determine if the areas are equal. In this case, without specific measurements, we assume that if the rectangle is divided in a way that can be proven to split the total area evenly (such as by parallel lines that proportionally divide the length and width), the parts can have equal areas even if they have different shapes.

Answer:

Lina is incorrect. Different - shaped parts of a rectangle can have equal areas. For example, if we divide a rectangle into two long thin rectangles and two square - like rectangles in a way that the sum of the lengths and widths are proportionally divided, the areas of the four parts can be equal.