Area Of A Triangle Worksheet: Practice Problems & Solutions

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11-15-2024

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To calculate the area of a triangle, one of the fundamental formulas we utilize is:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

This formula indicates that the area of a triangle is half the product of its base and height. But before diving into practice problems and solutions, let’s break down some crucial concepts regarding triangles and their areas.

Understanding Triangles

A triangle is a three-sided polygon, and it can be classified in different ways:

• By Sides:

  • Equilateral Triangle: All three sides are equal.
  • Isosceles Triangle: Two sides are equal.
  • Scalene Triangle: All sides are different.

• By Angles:

  • Acute Triangle: All angles are less than 90 degrees.
  • Right Triangle: One angle is exactly 90 degrees.
  • Obtuse Triangle: One angle is more than 90 degrees.

Each of these triangles can have its area calculated using the same formula mentioned above.

Key Terminology

• Base: The bottom side of the triangle, which can be any one of its sides.
• Height: The perpendicular line segment from the vertex opposite the base to the line that forms the base.

Now that we have some background on triangles and their key characteristics, let’s dive into practice problems to enhance understanding.

Practice Problems

Here are some problems designed to test and practice your understanding of calculating the area of triangles:

Problem 1: Right Triangle

A right triangle has a base of 6 cm and a height of 4 cm. What is the area?

Problem 2: Isosceles Triangle

An isosceles triangle has a base of 10 cm and a height of 8 cm. Calculate the area.

Problem 3: Scalene Triangle

A scalene triangle has sides measuring 7 cm, 8 cm, and 5 cm. The height corresponding to the base of 7 cm is 4.5 cm. Find the area.

Problem 4: Equilateral Triangle

An equilateral triangle has a side length of 12 cm. Find the area (use the formula for area in terms of side length).

Solutions to Practice Problems

Solution 1

For the right triangle:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 4 = \frac{24}{2} = 12 , \text{cm}^2 ]

Solution 2

For the isosceles triangle:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 8 = \frac{80}{2} = 40 , \text{cm}^2 ]

Solution 3

For the scalene triangle:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 4.5 = \frac{31.5}{2} = 15.75 , \text{cm}^2 ]

Solution 4

For the equilateral triangle, the area can also be calculated with the formula:

[ \text{Area} = \frac{\sqrt{3}}{4} \times \text{side}^2 = \frac{\sqrt{3}}{4} \times 12^2 = \frac{\sqrt{3}}{4} \times 144 = 36\sqrt{3} , \text{cm}^2 \approx 62.35 , \text{cm}^2 ]

Summary

In this worksheet, we covered the basic formulas for calculating the area of different types of triangles. The hands-on practice problems allow learners to deepen their understanding of the topic. To wrap up:

This table neatly summarizes the areas of different triangles calculated in our problems. Remember, practice is essential in mastering the concept of area. Keep practicing with different values, and you’ll find yourself becoming more comfortable with these calculations! 🌟