The Lengths Of The Bases Of A Trapezoid Are 9 Meters And 16 Meters. The Trapezoid Has An Area Of 150 Square Meters. What Is The Height, H H H , Of The Trapezoid?A. H = 12 M H = 12 \, \text{m} H = 12 M B. H = 13.6 M H = 13.6 \, \text{m} H = 13.6 M C. $h =
Understanding the Problem
The problem involves finding the height of a trapezoid given its area and the lengths of its bases. To solve this problem, we need to use the formula for the area of a trapezoid, which is:
Area = (1/2) × (sum of the lengths of the bases) × height
In this case, the area of the trapezoid is 150 square meters, and the lengths of its bases are 9 meters and 16 meters.
Formula for the Area of a Trapezoid
The formula for the area of a trapezoid is:
A = (1/2) × (a + b) × h
where A is the area, a and b are the lengths of the bases, and h is the height.
Substituting the Given Values
We are given that the area of the trapezoid is 150 square meters, and the lengths of its bases are 9 meters and 16 meters. We can substitute these values into the formula:
150 = (1/2) × (9 + 16) × h
Simplifying the Equation
We can simplify the equation by first finding the sum of the lengths of the bases:
9 + 16 = 25
Now, we can substitute this value back into the equation:
150 = (1/2) × 25 × h
Solving for the Height
To solve for the height, we can start by multiplying both sides of the equation by 2 to eliminate the fraction:
300 = 25 × h
Next, we can divide both sides of the equation by 25 to isolate the height:
h = 300 / 25
h = 12
Conclusion
The height of the trapezoid is 12 meters.
Discussion
The problem involves finding the height of a trapezoid given its area and the lengths of its bases. We used the formula for the area of a trapezoid to solve for the height. The formula is:
A = (1/2) × (a + b) × h
where A is the area, a and b are the lengths of the bases, and h is the height.
Example
Let's consider an example to illustrate how to use the formula. Suppose we have a trapezoid with an area of 200 square meters and bases of length 10 meters and 20 meters. We can use the formula to find the height:
200 = (1/2) × (10 + 20) × h
200 = (1/2) × 30 × h
400 = 30 × h
h = 400 / 30
h = 13.33
Conclusion
In this article, we discussed how to find the height of a trapezoid given its area and the lengths of its bases. We used the formula for the area of a trapezoid to solve for the height. The formula is:
A = (1/2) × (a + b) × h
where A is the area, a and b are the lengths of the bases, and h is the height.
Final Answer
The final answer is h = 12.
Q: What is the formula for the area of a trapezoid?
A: The formula for the area of a trapezoid is:
A = (1/2) × (a + b) × h
where A is the area, a and b are the lengths of the bases, and h is the height.
Q: How do I find the height of a trapezoid given its area and the lengths of its bases?
A: To find the height of a trapezoid, you can use the formula for the area of a trapezoid and solve for the height. Here's the step-by-step process:
- Write down the formula for the area of a trapezoid: A = (1/2) × (a + b) × h
- Substitute the given values into the formula: A = (1/2) × (a + b) × h
- Simplify the equation by finding the sum of the lengths of the bases: a + b
- Substitute the sum of the lengths of the bases back into the equation: A = (1/2) × (a + b) × h
- Multiply both sides of the equation by 2 to eliminate the fraction: 2A = (a + b) × h
- Divide both sides of the equation by (a + b) to isolate the height: h = 2A / (a + b)
Q: What if I have a trapezoid with an area of 200 square meters and bases of length 10 meters and 20 meters? How do I find the height?
A: To find the height of the trapezoid, you can use the formula:
h = 2A / (a + b)
Substitute the given values into the formula:
h = 2 × 200 / (10 + 20)
h = 400 / 30
h = 13.33
Q: Can I use the formula for the area of a trapezoid to find the height of a trapezoid with a negative area?
A: No, you cannot use the formula for the area of a trapezoid to find the height of a trapezoid with a negative area. The area of a trapezoid must be a positive value.
Q: What if I have a trapezoid with an area of 0 square meters? How do I find the height?
A: If the area of the trapezoid is 0 square meters, then the height of the trapezoid is also 0 meters.
Q: Can I use the formula for the area of a trapezoid to find the height of a trapezoid with a non-integer area?
A: Yes, you can use the formula for the area of a trapezoid to find the height of a trapezoid with a non-integer area. However, you may need to use a calculator or a computer program to perform the calculations.
Q: What if I have a trapezoid with an area of 150 square meters and bases of length 9 meters and 16 meters? How do I find the height?
A: To find the height of the trapezoid, you can use the formula:
h = 2A / (a + b)
Substitute the given values into the formula:
h = 2 × 150 / (9 + 16)
h = 300 / 25
h = 12
Conclusion
In this article, we discussed frequently asked questions about the height of a trapezoid. We covered topics such as the formula for the area of a trapezoid, how to find the height of a trapezoid given its area and the lengths of its bases, and what to do if you have a trapezoid with a negative area or a non-integer area. We also provided examples to illustrate how to use the formula to find the height of a trapezoid.