Area of Triangle on the Coordinate Plane Game

Area of Triangle on the Coordinate Plane Game
In Triangle Tech, you play as a “Coordinate Cadet” tasked with calculating the area of various triangular sectors on a grid. The goal is to complete a 10-question mission with the highest accuracy possible. Scroll down the page for a more detailed explanation.
 

 

How to Play the Area of Triangle on the Coordinate Plane Game
Core Mechanics
The game revolves around finding the area (A) of triangles using their coordinates (x, y).
Select a Mission: Choose your difficulty level from the main menu.
Analyze the Data: You are given the coordinates for three vertices (V1, V2, V3).
Calculate the Area: Use geometry formulas to determine the total units squared (u²).
Submit: Click the button corresponding to your answer. Correct answers glow Gold, while errors glow Red.

Mission Difficulties

Mission	Visuals	Triangle Types	Strategy
Standard	Grid + Plot	Right & Isosceles	Use \(Area = \frac{1}{2} \times base \times height\). Just count the squares on the grid.
Advanced	Grid + Plot	Oblique Scalene	The “Box Method”: Draw a rectangle around the triangle and subtract the outer corner triangles.
Elite	None (Data Only)	Any	Use the Shoelace Formula. Calculation without visual aid.

Methods to calculate the area of the triangle

1. The “Base and Height” Method
   Best for: Right triangles or triangles with one side perfectly horizontal or vertical.
   If one side of the triangle lies flat along a grid line, you can simply count the units to find the base and the height.
   Find the Base (b): Count the horizontal (or vertical) units of the flat side.
   Find the Height (h): Find the perpendicular distance from the base to the opposite vertex.
   Calculate: \(Area = \frac{1}{2} \times b \times h\)
   

2. The “Box” (Subtraction) Method
   Best for: Scalene or “tilted” triangles where no sides are horizontal or vertical.
   Instead of measuring the triangle directly, you build a rectangle (a “box”) around it that touches all three vertices.
   Draw a rectangle: Surround the triangle so that its sides are parallel to the x and y axes.
   Calculate the Box Area: Area = width × height.
   Subtract the corners: The “box” will create two or three right triangles in the corners outside your main triangle. Calculate their areas (which is easy since they are right triangles) and subtract them from the total box area.
   Main Area = (Area of Rectangle) - (Area of Triangle 1 + Area of Triangle 2 + Area of Triangle 3)
   

3. The Shoelace Formula
   Best for: Advanced missions or when you only have coordinates and no grid.
   This formula works for any triangle (or polygon) regardless of its shape or orientation. If your vertices are (x₁, y₁), (x₂, y₂), and (x₃, y₃):
   \(Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)
   How to use it:
   Multiply the x-coordinate of the first point by the difference of the y-coordinates of the other two points (in order).
   Repeat for the other two x-coordinates.
   Sum those results together.
   Take the absolute value (to make sure it’s positive).
   Divide by 2.
   

The video gives a clear, step-by-step approach to learn how to find the area of a triangle on the coordinate plane using the Shoelace Formula.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.