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
![**Finding the Area of an Isosceles Trapezoid**
**Problem:**
Find the area of the isosceles trapezoid shown below.
**Diagram:**
The provided diagram is an isosceles trapezoid with the following properties:
- The length of the shorter parallel side (top) is 7 units.
- The length of the longer parallel side (bottom) is 15 units.
- The height (perpendicular distance between the parallel sides) is 3 units.
- The non-parallel sides each have a length of 5 units.
7
________
/ \
/ \
5 /__________ \ 5
3
________________
15
**Options:**
1. 33 square units
2. 66 square units
3. 32 square units
4. 55 square units
---
**Solution:**
To find the area of a trapezoid, we use the formula:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Where:
- Base1 (\(b_1\)) = 7 units
- Base2 (\(b_2\)) = 15 units
- Height (\(h\)) = 3 units
Plugging these values into the formula gives:
\[ \text{Area} = \frac{1}{2} \times (7 + 15) \times 3 \]
\[ \text{Area} = \frac{1}{2} \times 22 \times 3 \]
\[ \text{Area} = \frac{1}{2} \times 66 \]
\[ \text{Area} = 33 \text{ square units} \]
Therefore, the area of the isosceles trapezoid is **33 square units**.
**Correct option:** 1. 33 square units](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5161d0-8c1c-4aef-9d6c-2e647d1b4222%2F7cfa5c15-35d8-4585-874f-bd10936e16de%2Fbj451mg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Area of an Isosceles Trapezoid**
**Problem:**
Find the area of the isosceles trapezoid shown below.
**Diagram:**
The provided diagram is an isosceles trapezoid with the following properties:
- The length of the shorter parallel side (top) is 7 units.
- The length of the longer parallel side (bottom) is 15 units.
- The height (perpendicular distance between the parallel sides) is 3 units.
- The non-parallel sides each have a length of 5 units.
7
________
/ \
/ \
5 /__________ \ 5
3
________________
15
**Options:**
1. 33 square units
2. 66 square units
3. 32 square units
4. 55 square units
---
**Solution:**
To find the area of a trapezoid, we use the formula:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Where:
- Base1 (\(b_1\)) = 7 units
- Base2 (\(b_2\)) = 15 units
- Height (\(h\)) = 3 units
Plugging these values into the formula gives:
\[ \text{Area} = \frac{1}{2} \times (7 + 15) \times 3 \]
\[ \text{Area} = \frac{1}{2} \times 22 \times 3 \]
\[ \text{Area} = \frac{1}{2} \times 66 \]
\[ \text{Area} = 33 \text{ square units} \]
Therefore, the area of the isosceles trapezoid is **33 square units**.
**Correct option:** 1. 33 square units
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