By considering total area as the sum of the areas of all of its parts, we can determine the area of a figure such as the one shown to the right. Find the total area of the figure to the right. 9 (a parallelogram and a triangle) 16 A = (Simplify your answer.)
By considering total area as the sum of the areas of all of its parts, we can determine the area of a figure such as the one shown to the right. Find the total area of the figure to the right. 9 (a parallelogram and a triangle) 16 A = (Simplify your answer.)
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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Find the total area of the figure
![**Instruction:**
To find the total area of the figure, which consists of a parallelogram and a triangle, we first determine the area of each individual part.
- **Parallelogram**: The base is labeled as 9 units, and the height is given as 3 units. The area of a parallelogram is calculated by multiplying the base by the height.
\[
\text{Area of parallelogram} = \text{base} \times \text{height} = 9 \times 3 = 27 \text{ square units}
\]
- **Triangle**: The base of the triangle is also 9 units (same as the parallelogram), but the height is labeled as 6 units. The area of a triangle is calculated using the formula:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 6 = 27 \text{ square units}
\]
**Total Area**:
To find the total area, sum the areas of the parallelogram and the triangle:
\[
\text{Total Area} = \text{Area of parallelogram} + \text{Area of triangle} = 27 + 27 = 54 \text{ square units}
\]
**Graph Explanation:**
The diagram represents a figure composed of a parallelogram and a triangle. Both shapes share the base of 9 units. The triangle extends beyond the parallelogram’s top side, with distinct heights (3 units for the parallelogram and 6 units for the triangle) marked by dashed lines.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F977ac1a7-2a1a-49aa-9358-74127afd8bcd%2F4040042a-f7af-4464-940d-8a873cc84415%2Fd6wp11j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
To find the total area of the figure, which consists of a parallelogram and a triangle, we first determine the area of each individual part.
- **Parallelogram**: The base is labeled as 9 units, and the height is given as 3 units. The area of a parallelogram is calculated by multiplying the base by the height.
\[
\text{Area of parallelogram} = \text{base} \times \text{height} = 9 \times 3 = 27 \text{ square units}
\]
- **Triangle**: The base of the triangle is also 9 units (same as the parallelogram), but the height is labeled as 6 units. The area of a triangle is calculated using the formula:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 6 = 27 \text{ square units}
\]
**Total Area**:
To find the total area, sum the areas of the parallelogram and the triangle:
\[
\text{Total Area} = \text{Area of parallelogram} + \text{Area of triangle} = 27 + 27 = 54 \text{ square units}
\]
**Graph Explanation:**
The diagram represents a figure composed of a parallelogram and a triangle. Both shapes share the base of 9 units. The triangle extends beyond the parallelogram’s top side, with distinct heights (3 units for the parallelogram and 6 units for the triangle) marked by dashed lines.
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