The Area of Acute Triangles Using Height and Base
Videos to help Grade 6 students find the area formula for a triangular region by decomposing a triangle into right triangles.
New York State Common Core Math Module 5, Grade 6, Lesson 3
Plans and Worksheets for Grade 6
Plans and Worksheets for all Grades
Lessons for Grade 6
Common Core For Grade 6
Lesson 3 Student Outcomes
Students show the area formula for a triangular region by decomposing a triangle into right triangles. For a given triangle, the height of the triangle is the length of the altitude. The length of the base is either called the length base or, more commonly, the base.
Students understand that the height of the triangle is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. The opposite side is called the base. Students understand that any side of a triangle can be considered a base and that the choice of base determines the height.
1. Work with a partner on the exercises below. Determine if the area formula A = 1/2 bh is always correct. You may use a calculator, but be sure to record your work on your paper as well.
2. Can we use the formula A = 1/2 x base x height to calculate the area of triangles that are not right triangles?
Explain your thinking.
3. Examine the given triangle and expression.
Explain what each part of the expression represents according to the triangle.
4. Joe found the area of a triangle by writing A = 1/2 (11 in.)(4 in.), while Kaitlyn found the area by writing A = 1/2 (3 in.)(4 in.) + 1/2 (8 in.)(4 in.). Explain how each student approached the problem.
5. The triangle below has an area of 4.76 sq. in. If the base is 3.4 in., let h be the height in inches.
a. Explain how the equation 4.76 in2
= 1/2(3.4 in.)(h) represents the situation.
b. Solve the equation.
Lessons 2 - 4
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.