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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Find the area of the shape shown below
![### Analyzing the Trapezoid
**Given Problem:**
Find the area of the shape shown below.
**Diagram Description:**
The diagram is a trapezoid, colored in purple, with the following dimensions:
- The top side (shorter base) measures 7.5 units.
- The bottom side (longer base) measures 12.5 units (7.5 + 5 unit increments from each side).
- The height (distance between the two bases) is 2.5 units.
### Calculating the Area of the Trapezoid
The formula for the area of a trapezoid is given by:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Where:
- \(\text{Base}_1\) is the length of the top side (7.5 units).
- \(\text{Base}_2\) is the length of the bottom side (12.5 units).
- \(\text{Height}\) is the perpendicular distance between the bases (2.5 units).
Substituting the given values:
\[ \text{Area} = \frac{1}{2} \times (7.5 + 12.5) \times 2.5 \]
\[ \text{Area} = \frac{1}{2} \times 20 \times 2.5 \]
\[ \text{Area} = 25 \text{ square units} \]
This calculation provides the area of the trapezoidal shape displayed in the diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d8d2b57-2a2c-4bce-8a34-d08276b564de%2F96dd575b-3aae-43d4-bb60-88a92ca9cf52%2Fg03eci_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing the Trapezoid
**Given Problem:**
Find the area of the shape shown below.
**Diagram Description:**
The diagram is a trapezoid, colored in purple, with the following dimensions:
- The top side (shorter base) measures 7.5 units.
- The bottom side (longer base) measures 12.5 units (7.5 + 5 unit increments from each side).
- The height (distance between the two bases) is 2.5 units.
### Calculating the Area of the Trapezoid
The formula for the area of a trapezoid is given by:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Where:
- \(\text{Base}_1\) is the length of the top side (7.5 units).
- \(\text{Base}_2\) is the length of the bottom side (12.5 units).
- \(\text{Height}\) is the perpendicular distance between the bases (2.5 units).
Substituting the given values:
\[ \text{Area} = \frac{1}{2} \times (7.5 + 12.5) \times 2.5 \]
\[ \text{Area} = \frac{1}{2} \times 20 \times 2.5 \]
\[ \text{Area} = 25 \text{ square units} \]
This calculation provides the area of the trapezoidal shape displayed in the diagram.
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