If The Area Of A Triangle Is 36 Inches And The Base Is 9 Inches What Is The Height Of The Triangle

Mar 10, 2025 by ADMIN 99 views

**If the Area of a Triangle is 36 Inches and the Base is 9 Inches: What is the Height of the Triangle?**

Understanding the Basics of a Triangle

A triangle is a polygon with three sides and three vertices. The area of a triangle can be calculated using the formula: Area = (base × height) / 2. In this article, we will use this formula to find the height of a triangle given its area and base.

The Formula for the Area of a Triangle

The formula for the area of a triangle is given by:

Area = (base × height) / 2

This formula is derived from the fact that the area of a triangle is equal to half the product of its base and height.

Given Values

We are given the following values:

Area of the triangle = 36 inches
Base of the triangle = 9 inches

Finding the Height of the Triangle

To find the height of the triangle, we can use the formula for the area of a triangle and rearrange it to solve for the height.

Rearranging the formula, we get:

height = (2 × Area) / base

Substituting the given values, we get:

height = (2 × 36) / 9

Calculating the Height

Now, let's calculate the height of the triangle:

height = (2 × 36) / 9 height = 72 / 9 height = 8 inches

Conclusion

Therefore, the height of the triangle is 8 inches.

Frequently Asked Questions (FAQs)

Q: What is the formula for the area of a triangle?

A: The formula for the area of a triangle is given by: Area = (base × height) / 2.

Q: How do I find the height of a triangle given its area and base?

A: To find the height of a triangle, you can use the formula: height = (2 × Area) / base.

Q: What is the relationship between the base and height of a triangle?

A: The base and height of a triangle are related by the formula: Area = (base × height) / 2.

Q: Can I use the formula for the area of a triangle to find the base of a triangle?

A: Yes, you can use the formula for the area of a triangle to find the base of a triangle by rearranging the formula to solve for the base.

Q: What is the unit of measurement for the height of a triangle?

A: The unit of measurement for the height of a triangle is the same as the unit of measurement for the base, which in this case is inches.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative base, as the base of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero base, as the base of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric base, as the base of a triangle must be a number.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric area?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric area, as the area of a triangle must be a number.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative area?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative area, as the area of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero area?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero area, as the area of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric height, as the height of a triangle must be a number.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative height, as the height of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero height, as the height of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric base and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric base and height, as the base and height of a triangle must be numbers.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative base and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative base and height, as the base and height of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero base and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero base and height, as the base and height of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric area and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric area and base, as the area and base of a triangle must be numbers.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative area and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative area and base, as the area and base of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero area and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero area and base, as the area and base of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric height and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric height and base, as the height and base of a triangle must be numbers.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative height and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative height and base, as the height and base of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero height and base?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero height and base, as the height and base of a triangle cannot be zero.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a non-numeric area, base, and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a non-numeric area, base, and height, as the area, base, and height of a triangle must be numbers.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a negative area, base, and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a negative area, base, and height, as the area, base, and height of a triangle cannot be negative.

Q: Can I use the formula for the area of a triangle to find the height of a triangle with a zero area, base, and height?

A: No, you cannot use the formula for the area of a triangle to find the height of a triangle with a zero area, base, and height, as the area, base, and height of a triangle cannot be zero.