Calculating The Area Of An Acute Triangle With Given Base And Height

Introduction

In geometry, finding the area of an acute triangle is essential for various applications. When you know the length of the base and the height of the triangle, calculating its area becomes straightforward. This guide will walk you through the process step-by-step, providing clear explanations and examples.

Understanding the Acute Triangle

An acute triangle is a triangle in which all three interior angles are acute, meaning they are less than 90 degrees.

The Formula for the Area of an Acute Triangle

The area $A$ of an acute triangle can be found using the formula:

$$A=\frac{1}{2}\times b\times h$$

Where:

- $b$ is the length of the base of the triangle.

- $h$ is the height of the triangle.

Explaining the Formula

To find the area of an acute triangle, we use the formula for the area of a triangle, which involves multiplying the length of the base by the height and then dividing by 2. This formula exploits the basic geometric relationship between the base, height, and area of a triangle.

Step-by-Step Calculation

Let's work through an example to illustrate the process.

Example:

Suppose we have an acute triangle with a base $b=10$ units and a height $h=6$ units. We want to find the area of the triangle.

Step 1: Identify the Given Values

Given:

- Base $b=10$ units

- Height $h=6$ units

Step 2: Use the Formula to Find the Area

Using the formula $A=\frac{1}{2}\times b\times h$, substitute the given values:

$$A=\frac{1}{2}\times 10\times 6$$

Step 3: Perform the Calculation

Now, calculate the area:

$$A=\frac{1}{2}\times 60$$

$$A=30$$

Final Value

For an acute triangle with a base $b=10$ units and a height $h=6$ units, the area is $30$ square units.

By following these steps, you can easily determine the area of an acute triangle when the base and height are given.