Calculating the Area of a Right Triangle

Oct 13, 2025 by miodeya.com 101 views

Understanding the Basics of Right Triangles

A right triangle is a type of triangle that has one angle equal to 90 degrees. This type of triangle is also known as a right-angled triangle. The area of a right triangle can be calculated using the formula: Area = (base × height) / 2. In this article, we will use this formula to calculate the area of a right triangle with a given height and base.

Calculating the Area of a Right Triangle

To calculate the area of a right triangle, we need to know the base and height of the triangle. The base of the triangle is the length of the side that is opposite the right angle, while the height of the triangle is the length of the side that is perpendicular to the base. In this case, the height of the triangle is $10 \frac{1}{2}$ feet and the base of the triangle is 33 feet.

Converting the Height to an Improper Fraction

Before we can calculate the area of the triangle, we need to convert the height from a mixed number to an improper fraction. To do this, we multiply the whole number part of the mixed number by the denominator, and then add the numerator. In this case, the height is $10 \frac{1}{2}$ feet, which is equal to $\frac{(10 \times 2) + 1}{2} = \frac{21}{2}$ feet.

Calculating the Area of the Triangle

Now that we have the height and base of the triangle, we can calculate the area of the triangle using the formula: Area = (base × height) / 2. Plugging in the values, we get: Area = (33 × $\frac{21}{2}$ ) / 2.

Simplifying the Expression

To simplify the expression, we can multiply the numerator and denominator by 2, which gives us: Area = (33 × 21) / 4.

Calculating the Numerator

To calculate the numerator, we multiply 33 by 21, which gives us: 33 × 21 = 693.

Calculating the Area

Now that we have the numerator, we can calculate the area by dividing the numerator by 4: Area = 693 / 4 = 173.25.

Converting the Answer to a Mixed Number

To convert the answer to a mixed number, we can divide the numerator by the denominator, which gives us: 173 ÷ 4 = 43 with a remainder of 1. Therefore, the area of the triangle is $43 \frac{1}{4}$ square feet.

Conclusion

In this article, we calculated the area of a right triangle with a given height and base. We used the formula: Area = (base × height) / 2 to calculate the area, and then simplified the expression to get the final answer. The area of the triangle is $43 \frac{1}{4}$ square feet.

Answer

The final answer is $43 \frac{1}{4} \, \text{ft}^2$ .

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

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

Q: What is the base of a right triangle?

A: The base of a right triangle is the length of the side that is opposite the right angle.

Q: What is the height of a right triangle?

A: The height of a right triangle is the length of the side that is perpendicular to the base.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number part of the mixed number by the denominator, and then add the numerator. For example, to convert $10 \frac{1}{2}$ to an improper fraction, you would multiply 10 by 2 and add 1, which gives you $\frac{21}{2}$ .

Q: Can I use a calculator to calculate the area of a right triangle?

A: Yes, you can use a calculator to calculate the area of a right triangle. Simply plug in the values for the base and height, and the calculator will give you the area.

Q: What if the base and height of the triangle are not given?

A: If the base and height of the triangle are not given, you will need to use other methods to find the area. This may involve using the Pythagorean theorem to find the length of the hypotenuse, or using trigonometry to find the angles of the triangle.

Q: Can I use the area of a right triangle to find the length of the base or height?

A: Yes, you can use the area of a right triangle to find the length of the base or height. If you know the area and one of the other values, you can plug in the values and solve for the unknown value.

Q: What if the triangle is not a right triangle?

A: If the triangle is not a right triangle, you will need to use different methods to find the area. This may involve using the formula for the area of a triangle, which is: Area = (base × height) / 2, but you will need to use the lengths of the sides of the triangle to find the base and height.

Q: Can I use the area of a triangle to find the perimeter of the triangle?

A: Yes, you can use the area of a triangle to find the perimeter of the triangle. If you know the area and the lengths of the sides of the triangle, you can use the formula for the area to find the length of the base or height, and then use the Pythagorean theorem to find the length of the hypotenuse.

Conclusion

In this article, we have answered some of the most frequently asked questions about the area of a right triangle. We have covered topics such as the formula for calculating the area, the base and height of a right triangle, and how to convert a mixed number to an improper fraction. We have also discussed how to use the area of a right triangle to find the length of the base or height, and how to use the area to find the perimeter of the triangle.