Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Sure, let's break down each part of the question step-by-step.
### 1. Finding the Height of a Triangle
We are given:
- Area of the triangle, [tex]\( A = 27 \, \text{ft}^2 \)[/tex]
- Base of the triangle, [tex]\( b = 9 \, \text{ft} \)[/tex]
The formula for the area of a triangle is:
[tex]\[ A = \frac{1}{2} b \cdot h \][/tex]
To find the height ([tex]\( h \)[/tex]), we can rearrange the formula:
[tex]\[ h = \frac{2A}{b} \][/tex]
Substitute the given values:
[tex]\[ h = \frac{2 \cdot 27}{9} = \frac{54}{9} = 6 \, \text{ft} \][/tex]
So, the height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].
The choices were:
- [tex]\( 243 \, \text{ft} \)[/tex]
- [tex]\( 6 \, \text{ft} \)[/tex] (Correct choice)
- [tex]\( 121.5 \, \text{ft} \)[/tex]
### 2. Finding the Area of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 4 \, \text{cm} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 5 \, \text{cm} \)[/tex]
- Height of the trapezoid, [tex]\( h = 3 \, \text{cm} \)[/tex]
The formula for the area of a trapezoid is:
[tex]\[ A = \frac{1}{2} (b_1 + b_2) \cdot h \][/tex]
Substitute the given values:
[tex]\[ A = \frac{1}{2} (4 + 5) \cdot 3 = \frac{1}{2} \cdot 9 \cdot 3 = \frac{27}{2} = 13.5 \, \text{cm}^2 \][/tex]
So, the area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].
The choices were:
- [tex]\( 13.5 \, \text{cm}^2 \)[/tex] (Correct choice)
- [tex]\( 30 \, \text{cm}^2 \)[/tex]
- [tex]\( 27 \, \text{cm}^2 \)[/tex]
- [tex]\( 6 \, \text{cm}^2 \)[/tex]
### 3. Finding the Height of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 9 \, \text{yd} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 12 \, \text{yd} \)[/tex]
- Area of the trapezoid, [tex]\( A = 21 \, \text{square yards} \)[/tex]
The formula for the height of a trapezoid is:
[tex]\[ h = \frac{2A}{b_1 + b_2} \][/tex]
Substitute the given values:
[tex]\[ h = \frac{2 \cdot 21}{9 + 12} = \frac{42}{21} = 2 \, \text{yd} \][/tex]
So, the height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].
The choices were:
- [tex]\( 5 \, \text{yd} \)[/tex]
- [tex]\( 220.5 \, \text{yd} \)[/tex]
- [tex]\( 1 \, \text{yd} \)[/tex]
- [tex]\( 2 \, \text{yd} \)[/tex] (Correct choice)
To summarize:
1. The height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].
2. The area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].
3. The height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].
### 1. Finding the Height of a Triangle
We are given:
- Area of the triangle, [tex]\( A = 27 \, \text{ft}^2 \)[/tex]
- Base of the triangle, [tex]\( b = 9 \, \text{ft} \)[/tex]
The formula for the area of a triangle is:
[tex]\[ A = \frac{1}{2} b \cdot h \][/tex]
To find the height ([tex]\( h \)[/tex]), we can rearrange the formula:
[tex]\[ h = \frac{2A}{b} \][/tex]
Substitute the given values:
[tex]\[ h = \frac{2 \cdot 27}{9} = \frac{54}{9} = 6 \, \text{ft} \][/tex]
So, the height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].
The choices were:
- [tex]\( 243 \, \text{ft} \)[/tex]
- [tex]\( 6 \, \text{ft} \)[/tex] (Correct choice)
- [tex]\( 121.5 \, \text{ft} \)[/tex]
### 2. Finding the Area of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 4 \, \text{cm} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 5 \, \text{cm} \)[/tex]
- Height of the trapezoid, [tex]\( h = 3 \, \text{cm} \)[/tex]
The formula for the area of a trapezoid is:
[tex]\[ A = \frac{1}{2} (b_1 + b_2) \cdot h \][/tex]
Substitute the given values:
[tex]\[ A = \frac{1}{2} (4 + 5) \cdot 3 = \frac{1}{2} \cdot 9 \cdot 3 = \frac{27}{2} = 13.5 \, \text{cm}^2 \][/tex]
So, the area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].
The choices were:
- [tex]\( 13.5 \, \text{cm}^2 \)[/tex] (Correct choice)
- [tex]\( 30 \, \text{cm}^2 \)[/tex]
- [tex]\( 27 \, \text{cm}^2 \)[/tex]
- [tex]\( 6 \, \text{cm}^2 \)[/tex]
### 3. Finding the Height of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 9 \, \text{yd} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 12 \, \text{yd} \)[/tex]
- Area of the trapezoid, [tex]\( A = 21 \, \text{square yards} \)[/tex]
The formula for the height of a trapezoid is:
[tex]\[ h = \frac{2A}{b_1 + b_2} \][/tex]
Substitute the given values:
[tex]\[ h = \frac{2 \cdot 21}{9 + 12} = \frac{42}{21} = 2 \, \text{yd} \][/tex]
So, the height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].
The choices were:
- [tex]\( 5 \, \text{yd} \)[/tex]
- [tex]\( 220.5 \, \text{yd} \)[/tex]
- [tex]\( 1 \, \text{yd} \)[/tex]
- [tex]\( 2 \, \text{yd} \)[/tex] (Correct choice)
To summarize:
1. The height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].
2. The area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].
3. The height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
