A rectangular piece of paper is 21 cm long and 15 cm wide. What is its area?
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- If you are given three vertices of a rectangle in a plane, how can you find the coordinates of the fourth vertex and the area of the rectangle?
- Consider a rectangle whose diagonals intersect at a point $(h, k)$ and whose sides are parallel to the coordinate axes. If the length of the diagonal is $2d$, what can you say about the possible areas of the rectangle?
- How is the concept of area used in agriculture?
- How is the concept of area used in art and design, for example, in composition and layout of rectangular canvases or frames?
- Consider a rectangle in the complex plane with vertices $z_1, z_2, z_3, z_4$. How can you find its area using complex numbers?
- What is the formula for the area of a rectangle?
- How is the diagonal of a rectangle related to its length and width?
- A rectangle has its vertices on the curve of a function. How can you find the maximum possible area of such a rectangle?
- How can the area of a rectangle be used to explain the concept of density (density = mass/volume, or population/area)?
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