Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Educational Website Content**
---
**Title: Calculating the Area of a Shaded Region in a Rectangular Grid**
---
**Introduction to the Problem:**
The following problem provides a rectangular grid with a shaded region. The task is to calculate the area, in square units, of the shaded part of the grid.
**Problem Statement:**
The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded part?
(Image Description: The image contains a rectangular grid divided into small squares. The grid has a shaded triangular region that starts from one corner of the rectangle and extends diagonally to the opposite corner. The remaining portion of the rectangle is unshaded. The task is to find the area of this shaded triangular part.)
**Visual Representation:**
- The grid is composed of 8 squares across the width (horizontal direction) and 8 squares across the height (vertical direction).
- The shaded region forms one half of the rectangle, divided along the diagonal connecting two opposite corners.
**Understanding the Dimensions:**
The total area of the rectangle can be found by multiplying the number of squares along the width (8 squares) by the number of squares along the height (8 squares):
\[ \text{Total Area of Rectangle} = 8 \text{ squares} \times 8 \text{ squares} = 64 \text{ square units} \]
Since the diagonal divides the rectangle into two equal areas, the shaded part is exactly half of the total area of the rectangle:
\[ \text{Area of Shaded Region} = \frac{1}{2} \times \text{Total Area of Rectangle} = \frac{1}{2} \times 64 \text{ square units} = 32 \text{ square units} \]
**Conclusion:**
Thus, the area of the shaded part of the rectangle is **32 square units**.
---
This example helps in understanding how to calculate the area of shapes within a grid by dividing them into simpler components or using symmetrical properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb223a19b-0fd0-443c-881a-6f762159fad5%2F7f894495-07b8-4036-afa3-afd147ba60ae%2Fuphnykn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
---
**Title: Calculating the Area of a Shaded Region in a Rectangular Grid**
---
**Introduction to the Problem:**
The following problem provides a rectangular grid with a shaded region. The task is to calculate the area, in square units, of the shaded part of the grid.
**Problem Statement:**
The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded part?
(Image Description: The image contains a rectangular grid divided into small squares. The grid has a shaded triangular region that starts from one corner of the rectangle and extends diagonally to the opposite corner. The remaining portion of the rectangle is unshaded. The task is to find the area of this shaded triangular part.)
**Visual Representation:**
- The grid is composed of 8 squares across the width (horizontal direction) and 8 squares across the height (vertical direction).
- The shaded region forms one half of the rectangle, divided along the diagonal connecting two opposite corners.
**Understanding the Dimensions:**
The total area of the rectangle can be found by multiplying the number of squares along the width (8 squares) by the number of squares along the height (8 squares):
\[ \text{Total Area of Rectangle} = 8 \text{ squares} \times 8 \text{ squares} = 64 \text{ square units} \]
Since the diagonal divides the rectangle into two equal areas, the shaded part is exactly half of the total area of the rectangle:
\[ \text{Area of Shaded Region} = \frac{1}{2} \times \text{Total Area of Rectangle} = \frac{1}{2} \times 64 \text{ square units} = 32 \text{ square units} \]
**Conclusion:**
Thus, the area of the shaded part of the rectangle is **32 square units**.
---
This example helps in understanding how to calculate the area of shapes within a grid by dividing them into simpler components or using symmetrical properties.
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