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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![### Finding the Area of Composite Figures
When tasked with finding the area of certain composite figures, we can utilize fundamental geometric formulas. Below is an example of a composite figure with its corresponding dimensions.
#### Diagram Explanation:
The figure is made up of a triangle and a rectangle sharing two common sides.
- A right triangle is positioned adjacent to a rectangle.
- The dimensions of the triangle are provided: height = 3 yards and base = 4 yards.
- The rectangle has an adjacent side to the triangle with a length of 5 yards.
- The entire length of the composite figure from the far left of the triangle to the far right of the rectangle is 8 yards.
- The hypotenuse of the triangle measures 12 yards.
#### Problem Statement:
Use formulas to find the area of the given figure.
#### Multiple Choice Options:
A. 18 yd²
B. 12 yd²
C. 24 yd²
D. 7.5 yd²
To calculate the area:
1. Calculate the area of the right triangle using the formula:
\[
\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
With the given base of 3 yards and height of 4 yards:
\[
\text{Area of Triangle} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ yd}^2
\]
2. Calculate the area of the rectangle using the formula:
\[
\text{Area of Rectangle} = \text{length} \times \text{width}
\]
With the given length of 5 yards and width of 4 yards:
\[
\text{Area of Rectangle} = 5 \times 4 = 20 \text{ yd}^2
\]
3. Add the areas of both shapes together to determine the total composite area:
\[
\text{Total Area} = \text{Area of Triangle} + \text{Area of Rectangle} = 6 \text{ yd}^2 + 20 \text{ yd}^2 = 26 \text{ yd}^2
\]
#### Conclusion:
The correct answer to the problem is not explicitly listed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd56393ec-45a8-472c-a036-5628b5e0585a%2F856cde95-a977-4438-9772-f68fd7d80d69%2F9dogmy2.png&w=3840&q=75)
Transcribed Image Text:### Finding the Area of Composite Figures
When tasked with finding the area of certain composite figures, we can utilize fundamental geometric formulas. Below is an example of a composite figure with its corresponding dimensions.
#### Diagram Explanation:
The figure is made up of a triangle and a rectangle sharing two common sides.
- A right triangle is positioned adjacent to a rectangle.
- The dimensions of the triangle are provided: height = 3 yards and base = 4 yards.
- The rectangle has an adjacent side to the triangle with a length of 5 yards.
- The entire length of the composite figure from the far left of the triangle to the far right of the rectangle is 8 yards.
- The hypotenuse of the triangle measures 12 yards.
#### Problem Statement:
Use formulas to find the area of the given figure.
#### Multiple Choice Options:
A. 18 yd²
B. 12 yd²
C. 24 yd²
D. 7.5 yd²
To calculate the area:
1. Calculate the area of the right triangle using the formula:
\[
\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
With the given base of 3 yards and height of 4 yards:
\[
\text{Area of Triangle} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ yd}^2
\]
2. Calculate the area of the rectangle using the formula:
\[
\text{Area of Rectangle} = \text{length} \times \text{width}
\]
With the given length of 5 yards and width of 4 yards:
\[
\text{Area of Rectangle} = 5 \times 4 = 20 \text{ yd}^2
\]
3. Add the areas of both shapes together to determine the total composite area:
\[
\text{Total Area} = \text{Area of Triangle} + \text{Area of Rectangle} = 6 \text{ yd}^2 + 20 \text{ yd}^2 = 26 \text{ yd}^2
\]
#### Conclusion:
The correct answer to the problem is not explicitly listed
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