What two figures do I draw such that the first one has a greater perimeter but smaller area than the second.
The first one, the smaller, could be a square.
t
To find two figures that have different perimeter but area relationships, we need to consider the properties of different shapes. Let's explore two examples: a square and a rectangle.
1. Square:
- A square has all equal sides, so let's choose a side length of 4 units.
- The perimeter of a square is calculated by summing all four sides, so the perimeter of this square would be 4 + 4 + 4 + 4 = 16 units.
- The area of a square is given by multiplying the lengths of two sides, so the area would be 4 × 4 = 16 square units.
2. Rectangle:
- Let's now consider a rectangle with different side lengths. For this example, let's use the dimensions of a 2-unit width and 8-unit length.
- The perimeter of a rectangle is found by adding all four sides, so the perimeter of this rectangle would be 2 + 2 + 8 + 8 = 20 units.
- The area of a rectangle is determined by multiplying the width and length, so the area would be 2 × 8 = 16 square units.
Thus, in this case, the rectangle has a greater perimeter (20 units) but a smaller area (16 square units) compared to the square (perimeter of 16 units and area of 16 square units).
In general, to find various examples that fit your criteria, you can pick two different shapes (e.g., square and rectangle, triangle and circle, etc.), choose their dimensions accordingly, and then calculate their perimeters and areas to compare them.