# +26 Lesson 2 Skills Practice Area Of Triangles Answer Key

## Introduction

Welcome to lesson 2 skills practice area of triangles answer key! In this article, we will be exploring the different skills and concepts related to finding the area of triangles. By understanding and mastering these skills, you will be able to solve various problems and questions involving triangles with ease. So, let's dive in and explore the answer key for lesson 2 skills practice area of triangles!

### 1. Understanding the Basics

Before we jump into the answer key, let's quickly review the basics of triangles. A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles can be classified based on their angles (acute, obtuse, or right) or their sides (equilateral, isosceles, or scalene).

### 2. Finding the Area of a Triangle

The area of a triangle can be calculated using the formula: Area = (base * height) / 2. The base is the length of the side of the triangle that is perpendicular to the height. The height is the perpendicular distance from the base to the opposite vertex.

### 3. Applying the Formula

Now, let's apply the formula to solve some practice problems. Remember to substitute the given values for the base and height into the formula and simplify the expression to find the area of the triangle.

### 4. Example Problem 1

Given: Base = 8 cm, Height = 6 cm

Substituting the values into the formula, we get: Area = (8 cm * 6 cm) / 2 = 48 cm²

Therefore, the area of the triangle is 48 square centimeters.

### 5. Example Problem 2

Given: Base = 12 in, Height = 9 in

Substituting the values into the formula, we get: Area = (12 in * 9 in) / 2 = 54 in²

Therefore, the area of the triangle is 54 square inches.

### 6. Example Problem 3

Given: Base = 5 m, Height = 3 m

Substituting the values into the formula, we get: Area = (5 m * 3 m) / 2 = 7.5 m²

Therefore, the area of the triangle is 7.5 square meters.

### 7. Solving for Missing Values

Sometimes, you may be given the area of a triangle and asked to find either the base or the height. In such cases, you can rearrange the formula to solve for the missing value.

### 8. Example Problem 4

Given: Area = 36 cm², Height = ?

Rearranging the formula, we get: Height = (2 * Area) / Base

Substituting the given values, we get: Height = (2 * 36 cm²) / Base

Let's assume the base is 12 cm.

Substituting the value of the base, we get: Height = (2 * 36 cm²) / 12 cm = 6 cm

Therefore, the height of the triangle is 6 centimeters.

### 9. Example Problem 5

Given: Area = 45 in², Base = ?

Rearranging the formula, we get: Base = (2 * Area) / Height

Substituting the given values, we get: Base = (2 * 45 in²) / Height

Let's assume the height is 9 inches.

Substituting the value of the height, we get: Base = (2 * 45 in²) / 9 in = 10 in

Therefore, the base of the triangle is 10 inches.

### 10. Special Cases

In some cases, you may encounter triangles that are not right triangles or triangles with special properties. Let's explore a few special cases and how to find their areas.

### 11. Equilateral Triangles

An equilateral triangle is a triangle with all three sides equal in length. To find the area of an equilateral triangle, you can use the formula: Area = (√3 / 4) * side². Here, side represents the length of any side of the triangle.

### 12. Example Problem 6

Given: Side = 6 cm

Substituting the value into the formula, we get: Area = (√3 / 4) * 6 cm² ≈ 15.588 cm²

Therefore, the area of the equilateral triangle is approximately 15.588 square centimeters.

### 13. Isosceles Triangles

An isosceles triangle is a triangle with two sides equal in length. To find the area of an isosceles triangle, you can use the formula: Area = (1/4) * √(4a² - b²) * b, where a represents the length of the equal sides and b represents the length of the base.

### 14. Example Problem 7

Given: Equal Sides (a) = 5 cm, Base (b) = 8 cm

Substituting the values into the formula, we get: Area = (1/4) * √(4 * 5² - 8²) * 8 cm ≈ 15.491 cm²

Therefore, the area of the isosceles triangle is approximately 15.491 square centimeters.

### 15. Practical Applications

The concept of finding the area of triangles is not only limited to theoretical problems. It has various practical applications in fields such as architecture, engineering, and design. By understanding how to find the area of triangles, you will be able to solve real-world problems more effectively.

### 16. Conclusion

As we conclude our exploration of the lesson 2 skills practice area of triangles answer key, we hope that you have gained a clear understanding of the different skills and concepts related to finding the area of triangles. Remember to practice these skills regularly to enhance your problem-solving abilities. Happy learning!