Area of a Triangle With Vertices - Geometry

TL;DR

Learn how to find the area of a triangle using its three vertices by applying the formula and simplifying the expression.

Transcript

in this video we're going to talk about how to calculate the area of a triangle given the three vertices of the triangle so let's graph the triangle first so the first one is around negative 3 negative 2 which is somewhere in this region this is just a ballpark estimate and the second point is at 3 5 which is probably going to be somewhere over her... Read More

Key Insights

• 📈 Graphing the triangle is the first step in calculating its area using vertex coordinates.
• 🔺 The formula for finding the area of a triangle is 1/2 * |(x1 * y2) + (x2 * y3) + (x3 * y1) - (x1 * y3) - (x2 * y1) - (x3 * y2)|.
• 😑 Substituting the coordinates into the formula and simplifying the expression will yield the area of the triangle.
• ❓ The absolute value ensures the area is always positive.
• 💁 The final answer can be written as a fraction (75/2) or in decimal form (37.5 square units).
• 🆘 The content creator offers help in various subjects like geometry, algebra, trigonometry, calculus, chemistry, and physics.
• 🎮 The video is part of a playlist on the content creator's channel, categorized by subject.

Questions & Answers

Q: What is the first step in calculating the area of a triangle given its vertices?

The first step is to graph the triangle using its three vertices and label them as points A, B, and C.

Q: How is the area of the triangle calculated using the formula?

The formula used is: 1/2 * |(x1 * y2) + (x2 * y3) + (x3 * y1) - (x1 * y3) - (x2 * y1) - (x3 * y2)|.

Q: Can the area of a triangle be negative?

No, the area of a triangle is always positive as the absolute value is taken in the formula.

Q: What are the coordinates used to calculate the area in the example?

In the example, the coordinates of the vertices are: A(-3, -2), B(3, 5), and C(6, -4).

Summary & Key Takeaways

• The video demonstrates how to graph a triangle given its three vertices and labels them as points A, B, and C.

• The formula for finding the area of the triangle is explained and applied step by step using the coordinates of the vertices.

• By substituting the coordinates into the formula and simplifying the expression, the area of the triangle is calculated to be 37.5 square units.