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Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 4, Lesson 9

Student Outcomes

- Students find the perimeter of a triangle in the coordinate plane using the distance formula.
- Students state and apply the formula for area of a triangle with vertices (0,0),(x1, y1), and (x2 , y2).

**Perimeter and Area of Triangles in the Cartesian Plane**

Classwork

**Opening Exercise**

Find the area of the shaded region

**Example**

Consider a triangular region in the plane with vertices 𝑂(0, 0), 𝐴(5, 2), and 𝐵(3, 4). What is the perimeter of the
triangular region?

What is the area of the triangular region?

Find the general formula for the area of the triangle with vertices 𝑂(0, 0), 𝐴(𝑥1, 𝑦1), and 𝐵(𝑥2, 𝑦2), as shown.
Does the formula work for this triangle?

**Exercise**

Find the area of the triangles with vertices listed, first by finding the area of the rectangle enclosing the triangle and
subtracting the area of the surrounding triangles, then by using the formula 1/2(𝑥1𝑦2− 𝑥2𝑦1).

a. 𝑂(0, 0), 𝐴(5, 6), 𝐵(4, 1)

b. 𝑂(0, 0), 𝐴(3, 2), 𝐵 (−2, 6)

c. 𝑂(0, 0), 𝐴(5,−3), 𝐵(−2, 6)

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