Triangle Area Worksheet with Solutions and Examples

Triangle Area Worksheet with Solutions and Examples

Calculating the area of a triangle is a fundamental concept in geometry and trigonometry. It is used to determine the size of the triangle, which can be useful in various mathematical and real-world applications. In this worksheet, we will provide you with examples and solutions to help you understand how to calculate the area of a triangle.

What is the Formula for the Area of a Triangle?

The formula for the area of a triangle is:

Area = (base × height) / 2

This formula is used when the base and height of the triangle are known. The base is the side of the triangle that is perpendicular to the height.

Example 1: Finding the Area of a Triangle with a Known Base and Height

Find the area of a triangle with a base of 5 cm and a height of 6 cm.

📝 Note: To find the area, we will use the formula: Area = (base × height) / 2

Solution:

Area = (5 cm × 6 cm) / 2 Area = 30 cm² / 2 Area = 15 cm²

Example 2: Finding the Area of a Triangle with a Known Base and Angle

Find the area of a triangle with a base of 8 cm and an angle of 60°. The height of the triangle is unknown.

📝 Note: To find the area, we will use the formula: Area = (base × height) / 2. Since the height is unknown, we will use trigonometry to find it.

Solution:

First, we need to find the height of the triangle using trigonometry:

sin(60°) = opposite side (height) / hypotenuse (base) sin(60°) = height / 8 cm height = 8 cm × sin(60°) height ≈ 6.93 cm

Now that we have the height, we can find the area:

Area = (base × height) / 2 Area = (8 cm × 6.93 cm) / 2 Area ≈ 27.48 cm²

Example 3: Finding the Area of a Triangle with Three Known Sides

Find the area of a triangle with sides of 7 cm, 8 cm, and 9 cm.

📝 Note: To find the area, we will use Heron's formula: Area = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter and a, b, and c are the sides of the triangle.

Solution:

First, we need to find the semi-perimeter:

s = (a + b + c) / 2 s = (7 cm + 8 cm + 9 cm) / 2 s = 12 cm

Now, we can use Heron’s formula to find the area:

Area = √(s(s - a)(s - b)(s - c)) Area = √(12 cm(12 cm - 7 cm)(12 cm - 8 cm)(12 cm - 9 cm)) Area ≈ 26.83 cm²

Table: Summary of Triangle Area Formulas

Conclusion:

Calculating the area of a triangle can be done using various formulas, depending on the information provided. By understanding these formulas and practicing with examples, you can become proficient in finding the area of triangles.

Frequently Asked Questions:

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