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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Transcribed Image Text:# Days 10 Final Check Point Quiz
## Composite Area Calculation
**Problem Statement:**
The area of the composite figure below is 91.7 square centimeters.
**Diagram Description:**
- The figure consists of a trapezoid and a triangle.
- The trapezoid has:
- A height of 5.3 cm
- One of its parallel sides is labeled as \( x \) cm
- The other parallel side is the sum of \( x \) cm and 9.8 cm
- The triangle has:
- A base of 9.8 cm
- A height of 7.2 cm
**Question:**
What is the value of \( x \)?
**Multiple Choice Options:**
1. About 7.8 cm
2. About 10.6 cm
3. About 12.4 cm
4. About 14.0 cm
### Explanation of Figures:
**Trapezoid:**
- The height is marked as 5.3 cm.
- The lengths of the parallel sides are \( x \) cm and \( x + 9.8 \) cm.
**Triangle:**
- The base length is 9.8 cm.
- The height is marked as 7.2 cm.
**Calculation Method:**
To find \( x \), you would generally use the formula for the area of a trapezoid and the area of a triangle joining the sum of the areas to equal the total area provided.
### Steps to Solve:
1. Calculate the area of the triangle.
2. Use the total composite area and the triangle area to find the remaining area that belongs to the trapezoid.
3. Solve for \( x \) using the trapezoid area formula.
By examining the structure and known measurements, you can determine the values and arrive at an accurate calculation for \( x \).
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