**Determine the fraction of the square in Figure 3.6 that is shaded. Explain your reasoning (attach all scratch work HERE).****Description of the Diagram:**The diagram features a square with one of its diagonals drawn. Additionally, a line connects the midpoint of the bottom edge to the opposite vertex on the top edge, creating a triangle within the square. This triangle is shaded, covering part of the area of the square. The task is to determine what fraction of the square's total area is covered by this shaded triangle.**Explanation:**To solve this, consider the following steps:1. **Identify Key Points and Lines:** - The square has vertices labeled at the top-left, top-right, bottom-left, and bottom-right. - The diagonal from the bottom-left to top-right divides the square into two equal right triangles. - The additional line from the midpoint of the bottom edge to the top-left vertex divides the left triangle.2. **Divide the Problem:** - The shaded area is the intersection of the two triangles created by the diagonal and the additional line.3. **Calculate Areas:** - The entire square has an area equal to the side length squared. - Each triangle formed by the diagonal has an area equal to half of the square's area. - The shaded triangle, being a right triangle with one leg half the length of the square's side, covers one quarter of the square's area.Therefore, the shaded triangle covers one quarter (1/4) of the square.

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Determine the fraction of the square in Figure 3.6 that is shaded. Explain your reasoning (attach all scratch work HERE).

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Determine the fraction of the square in Figure 3.6 that is shaded. Explain your reasoning (attach all scratch work HERE).**

**Description of the Diagram:**

The diagram features a square with one of its diagonals drawn. Additionally, a line connects the midpoint of the bottom edge to the opposite vertex on the top edge, creating a triangle within the square. This triangle is shaded, covering part of the area of the square.

The task is to determine what fraction of the square's total area is covered by this shaded triangle.

**Explanation:**

To solve this, consider the following steps:

1. **Identify Key Points and Lines:**
- The square has vertices labeled at the top-left, top-right, bottom-left, and bottom-right.
- The diagonal from the bottom-left to top-right divides the square into two equal right triangles.
- The additional line from the midpoint of the bottom edge to the top-left vertex divides the left triangle.

2. **Divide the Problem:**
- The shaded area is the intersection of the two triangles created by the diagonal and the additional line.

3. **Calculate Areas:**
- The entire square has an area equal to the side length squared.
- Each triangle formed by the diagonal has an area equal to half of the square's area.
- The shaded triangle, being a right triangle with one leg half the length of the square's side, covers one quarter of the square's area.

Therefore, the shaded triangle covers one quarter (1/4) of the square.

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