Explain why this parallelograms area will be less than the given rectangles area

The area of a parallelogram is given by the formula:

\[
\text{Area of Parallelogram} = \text{Base} \times \text{Height}
\]

Similarly, the area of a rectangle is given by:

\[
\text{Area of Rectangle} = \text{Length} \times \text{Width}
\]

In this case, the reason a parallelogram's area will be less than a rectangle's area, given the same base (or length) and width, lies in the **height** of the parallelogram. Here's why:

1. **Height in a Parallelogram**: The height of a parallelogram is measured as the perpendicular distance from one base to the opposite side. If the sides of the parallelogram are slanted (i.e., not at right angles), the perpendicular height is shorter than the side length itself.
   
2. **Rectangle's Height Equals Side Length**: In a rectangle, the height and width (or side lengths) are perpendicular by definition, meaning that the height of the rectangle is equal to its width.

So, even if the base (or length) of the parallelogram and the rectangle is the same, the parallelogram’s slanted sides reduce the effective height. A shorter height results in a smaller area when compared to the rectangle with the same base and side dimensions.

To summarize: The parallelogram's area is less than the rectangle's area because the height (measured perpendicular to the base) in the parallelogram is less than the width of the rectangle, leading to a smaller product when multiplying the base by height.

Would you like more details or have any further questions on this?

Here are five related questions to expand your understanding:
1. How does the angle between the sides of a parallelogram affect its height and area?
2. Can a parallelogram ever have the same area as a rectangle? If so, under what conditions?
3. How do you calculate the height of a parallelogram if you're only given the side lengths and angles?
4. What happens to the area of a parallelogram if the slant angle increases?
5. Can the area of a parallelogram be larger than the area of a rectangle if given different dimensions?

**Tip:** Always remember that the height of a parallelogram is the perpendicular distance to the base, not the length of its slanted side. This is key when calculating its area.

Explain why this parallelogram's area will be less than the given rectangle's area.

Understand why the area of a parallelogram is less than that of a rectangle, even when they share the same base and side lengths. Explore key geometry concepts, including height, base, and the difference between slanted and perpendicular measurements. Suitable for students in Grades 6-8.

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