Lesson Topic: The Area of Triangles Using Height and Base

Lesson Objective: I can…Justify the area formula for a

triangular region [1/2(base)(height)] by deconstructing a triangle into right triangles and showing the area of a right triangle is exactly one half the area of a rectangle.

Construct altitudes for all types of triangles.

Review How many different types of triangles

are there? What are they? What’s the formula to find the area of

a triangle? Does this formula work for all types

of triangles? True or false: Each triangle has 1

base & 1 height.

3

Right, acute, obtuse

½bh or bh/2

Yes

False, each triangles has 3 different options for a base and 3 different options for a height.

Review What do we know about right

triangles?

What do we know about acute triangles?

What do we know about obtuse triangles?

How do we find the area of a rectangle?

One interior angle must be exactly

90 degrees.

All interior angles are less than

90*.

One interior angle is greater than

90*.

bh

Vocabulary Altitude: A perpendicular line

segment from a vertex of a triangle to the line containing the opposite side. For every triangle, there are three choices for the altitude. The altitude doesn’t have to be a side of the triangle, and it may lie inside or outside of the triangle.

The height is the length of the altitude.

Base: The side opposite the vertex. **Base is not always the bottom and height is not always vertical.

Let’s construct altitudes for all types of triangles

1. Right2. Acute3. Obtuse

Options:1. Practice – Pull up exercises on

today’s PowerPoint on your iPad and record in your notebook or on a separate sheet of paper

2. Draw three triangles (acute, right, and obtuse) that have the same area. Explain how you know they have the same area.

3. Deconstruct acute and obtuse triangles into right triangles by cutting and re-arranging their parts like shown in lesson.

Exercises

Exercises, cont.

Exercises, cont.

Exercises, cont.

Lesson Summary

• We can use our knowledge of area to calculate the area of more complex shapes by splitting the shape into smaller shapes for which we know how to calculate the area.

Evaluate Your Learning4321

How will you “Sharpen Your Saw”?