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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![**Finding the Area of a Trapezoid**
In this activity, you are tasked with finding the area of the trapezoid shown in the diagram below.
**Diagram:**
- The diagram contains a trapezoid shaded in purple.
- One of the non-parallel sides is perpendicular to the base, indicated by the right angle marker.
- The longer base of the trapezoid (bottom side) measures 6 units.
- The shorter base of the trapezoid (top side) measures 1 unit.
- The perpendicular height from the shorter base to the longer base measures 12 units.
- The non-perpendicular side has a length of 13 units.
The formula to calculate the area of a trapezoid is:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
Where:
- \( b_1 \) and \( b_2 \) are the lengths of the two bases.
- \( h \) is the height.
**Given:**
- \( b_1 = 6 \) units
- \( b_2 = 1 \) unit
- \( h = 12 \) units
**Calculation:**
\[ \text{Area} = \frac{1}{2} \times (6 + 1) \times 12 \]
\[ \text{Area} = \frac{1}{2} \times 7 \times 12 \]
\[ \text{Area} = \frac{1}{2} \times 84 \]
\[ \text{Area} = 42 \text{ units}^2 \]
**Interactive Part:**
- There is a blank input field to enter your calculated area value in units\(^2\).
- Below that, a button labeled "Show Calculator" is available for additional assistance.
Make sure to verify your calculations using the interactive tools if needed!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cb7ebfc-d0c5-4532-b2f0-75a956d47556%2F26738de2-7efd-4c3e-82df-feaa5f36c0c6%2Fm802iz.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Area of a Trapezoid**
In this activity, you are tasked with finding the area of the trapezoid shown in the diagram below.
**Diagram:**
- The diagram contains a trapezoid shaded in purple.
- One of the non-parallel sides is perpendicular to the base, indicated by the right angle marker.
- The longer base of the trapezoid (bottom side) measures 6 units.
- The shorter base of the trapezoid (top side) measures 1 unit.
- The perpendicular height from the shorter base to the longer base measures 12 units.
- The non-perpendicular side has a length of 13 units.
The formula to calculate the area of a trapezoid is:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
Where:
- \( b_1 \) and \( b_2 \) are the lengths of the two bases.
- \( h \) is the height.
**Given:**
- \( b_1 = 6 \) units
- \( b_2 = 1 \) unit
- \( h = 12 \) units
**Calculation:**
\[ \text{Area} = \frac{1}{2} \times (6 + 1) \times 12 \]
\[ \text{Area} = \frac{1}{2} \times 7 \times 12 \]
\[ \text{Area} = \frac{1}{2} \times 84 \]
\[ \text{Area} = 42 \text{ units}^2 \]
**Interactive Part:**
- There is a blank input field to enter your calculated area value in units\(^2\).
- Below that, a button labeled "Show Calculator" is available for additional assistance.
Make sure to verify your calculations using the interactive tools if needed!
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