Question

Find the area \(A\) of a triangle with height 9 centimeters and base 4 centimeters.

Short answer

18 square centimeters

Step-by-step solution

Understand the Formula for the Area of a Triangle

The area of a triangle can be calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]Here, \(A\) is the area, the base is the length of the bottom side, and the height is the perpendicular distance from the base to the opposite vertex.

Identify the Given Values

In the problem, the height of the triangle is given as 9 centimeters, and the base of the triangle is given as 4 centimeters.

Plug the Values into the Formula

Substitute the values of the base and height into the formula: \[ A = \frac{1}{2} \times 4 \times 9 \]

Perform the Calculations

First, multiply the base and height: \[ 4 \times 9 = 36 \]Next, multiply by \(\frac{1}{2}\): \[ \frac{1}{2} \times 36 = 18 \]

Conclusion

The area of the triangle is 18 square centimeters.

Key concepts

triangle area formula

To calculate the area of a triangle, we use a specific formula that simplifies the task. The formula is \(A = \frac{1}{2} \times \text{base} \times \text{height}\). Here, \(A\) represents the area of the triangle. The base is one of the triangle's sides, and the height is the perpendicular distance from that base to the opposite vertex.
For example, if the base is 4 centimeters and the height is 9 centimeters, you plug these values into the formula like this: \(A = \frac{1}{2} \times 4 \times 9\). By simplifying this, you get \(A = \frac{1}{2} \times 36 = 18 \) square centimeters. This formula works for any triangle as long as you know the base and height.

geometry

Geometry is a fundamental branch of mathematics that deals with shapes, sizes, and the properties of space. In geometry, understanding the properties of different shapes, such as triangles, rectangles, and circles, is crucial.
Triangles are particularly important because they have unique properties. For instance, the sum of the interior angles of a triangle always equals 180 degrees. Additionally, knowing various methods to calculate areas and other measurements in triangles helps solve real-world problems effectively. Recognizing the base and height in a triangle is a key geometrical skill that helps in applying the area formula.

basic arithmetic

Basic arithmetic involves the simple operations of addition, subtraction, multiplication, and division. These operations form the backbone of more complex math topics.
In the context of calculating the area of a triangle, multiplication and division are used prominently. For example, when given a base of 4 centimeters and a height of 9 centimeters, you multiply these two numbers ( \( 4 \times 9 = 36 \) ). Then, you divide by 2 ( \( \frac{36}{2} = 18 \) ) to find the area.
Understanding arithmetic ensures that you can perform these calculations accurately and efficiently. This is essential not just for geometry, but for most mathematical problems you will encounter.