Explain the area formula for the following triangle. A. In particular explain how the formula for the area of a triangle is related to the formula for the area of the parallelogram? B. Explain why shearing certain shapes does not change their area? First explain what "shearing" means? How is this related to the formulas we have for a triangle and a parallelogram?

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Explain the area formula for the following triangle.

A. In particular explain how the formula for the area of a triangle is related to the formula for the area of the parallelogram? 

B. Explain why shearing certain shapes does not change their area? First explain what "shearing" means? How is this related to the formulas we have for a triangle and a parallelogram?

## Understanding the Area Formula for Triangles

### 7. Explain the Area Formula for the Following Triangle

**a. Relation to the Parallelogram:**
In particular, explain how the formula for the area of a triangle is related to the formula for the area of a parallelogram.

**b. Shearing and Area Preservation:**
Explain why shearing certain shapes does not change their area. First, explain what "shearing" means. How is this related to the formulas we have for a triangle and a parallelogram?

### Diagram Explanation

The diagram depicts a triangle. Here's a breakdown:

- **Base:** Represented by the red line at the bottom of the triangle.
- **Perpendicular Height:** Shown by the dotted line extending from a vertex perpendicular to the base.

This visualization helps in understanding how the area is calculated using base and height.
Transcribed Image Text:## Understanding the Area Formula for Triangles ### 7. Explain the Area Formula for the Following Triangle **a. Relation to the Parallelogram:** In particular, explain how the formula for the area of a triangle is related to the formula for the area of a parallelogram. **b. Shearing and Area Preservation:** Explain why shearing certain shapes does not change their area. First, explain what "shearing" means. How is this related to the formulas we have for a triangle and a parallelogram? ### Diagram Explanation The diagram depicts a triangle. Here's a breakdown: - **Base:** Represented by the red line at the bottom of the triangle. - **Perpendicular Height:** Shown by the dotted line extending from a vertex perpendicular to the base. This visualization helps in understanding how the area is calculated using base and height.
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