The area of a parallelogram is found by multiplying its base by its height ($Area = base \times height$). Remember, the height must be perpendicular to the base. For a triangle, the area is half the product of its base and height ($Area = \frac{1}{2} \times base \times height$). Understanding these formulas is key to solving many geometry problems!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Base | A. The perpendicular distance from the base to the opposite side or vertex. |
| 2. Height | B. A four-sided figure with opposite sides parallel. |
| 3. Parallelogram | C. Any side of a figure, usually the bottom side. |
| 4. Area | D. A polygon with three sides and three angles. |
| 5. Triangle | E. The amount of space inside a 2D shape. |
Complete the following sentences using the correct terms:
The area of a ____________ is calculated by multiplying the base by the ____________. The area of a ____________ is half the product of its base and height. In a parallelogram, opposite sides are ____________.
Explain, in your own words, why the formula for the area of a triangle is half the formula for the area of a parallelogram, assuming they share the same base and height. Provide a diagram to support your explanation.
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