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
Related questions
Question
Find the area of the following trapezoids:
![**Find the area of the following trapezoids**
**4.**
- Base 1: 5 units
- Base 2: 9 units
- Height: \( 6\sqrt{2} \) units (perpendicular height dropped from base 1)
- Angle near the height: \( 45^\circ \)
**5.**
- Base 1: \( \frac{5}{2}\sqrt{2} \) units
- Base 2: \( 11\sqrt{2} \) units
- Height: \( \frac{2}{2}\sqrt{2} \) units (perpendicular height dropped from base 1)
**6.**
- Base 1: 12 units
- Base 2: 24 units
- Height: 20 units
- Base of the trapezoid from the height is perpendicular to bases 1 and 2.
To find the area of a trapezoid, you can use the formula:
\[
\text{Area} = \frac{1}{2} \times (\text{Base 1} + \text{Base 2}) \times \text{Height}
\]
Using this formula, you can calculate the area of each trapezoid accurately.
**For example, the area of a trapezoid with bases \( a \) and \( b \) and height \( h \) is given by:**
\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\]
Now, applying the formula:
**4.**
\[
\text{Area} = \frac{1}{2} \times (5 + 9) \times 6\sqrt{2}
\]
**5.**
\[
\text{Area} = \frac{1}{2} \times \left(\frac{5}{2}\sqrt{2} + 11\sqrt{2}\right) \times \frac{2}{2}\sqrt{2}
\]
**6.**
\[
\text{Area} = \frac{1}{2} \times (12 + 24) \times 20
\]
By plugging in the values and performing the necessary calculations, you will obtain the areas of the given trapezoids.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9bce8c0-069b-44af-bdf7-a7daf1a8c7d3%2Fcf1d5134-648a-456c-bbc2-d658de1a02f4%2Fv0zmqc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the area of the following trapezoids**
**4.**
- Base 1: 5 units
- Base 2: 9 units
- Height: \( 6\sqrt{2} \) units (perpendicular height dropped from base 1)
- Angle near the height: \( 45^\circ \)
**5.**
- Base 1: \( \frac{5}{2}\sqrt{2} \) units
- Base 2: \( 11\sqrt{2} \) units
- Height: \( \frac{2}{2}\sqrt{2} \) units (perpendicular height dropped from base 1)
**6.**
- Base 1: 12 units
- Base 2: 24 units
- Height: 20 units
- Base of the trapezoid from the height is perpendicular to bases 1 and 2.
To find the area of a trapezoid, you can use the formula:
\[
\text{Area} = \frac{1}{2} \times (\text{Base 1} + \text{Base 2}) \times \text{Height}
\]
Using this formula, you can calculate the area of each trapezoid accurately.
**For example, the area of a trapezoid with bases \( a \) and \( b \) and height \( h \) is given by:**
\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\]
Now, applying the formula:
**4.**
\[
\text{Area} = \frac{1}{2} \times (5 + 9) \times 6\sqrt{2}
\]
**5.**
\[
\text{Area} = \frac{1}{2} \times \left(\frac{5}{2}\sqrt{2} + 11\sqrt{2}\right) \times \frac{2}{2}\sqrt{2}
\]
**6.**
\[
\text{Area} = \frac{1}{2} \times (12 + 24) \times 20
\]
By plugging in the values and performing the necessary calculations, you will obtain the areas of the given trapezoids.
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