1. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
1
May 27, 2014
Answers Problem Set Lesson 1

2. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
2
May 27, 2014

3. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
3
May 27, 2014

4. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
4
May 27, 2014

5. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
5
May 27, 2014

6. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
6
May 27, 2014
MODULE 5 Area, Surface Area, and Volume
Problems
Topic A: Area of Triangles, Quadrilaterals, and
Polygons
Lesson 2: The Area of Right Triangles
Student Outcomes
§ Students jusfy the area formula for a right triangle by viewing the right triangle as part of a rectangle composed of two right triangles.

7. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
7
May 27, 2014
a = bh4cm
9cm
a =4cm
9cm

8. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
8
May 27, 2014
p. 7

9. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
9
May 27, 2014
MODULE 5 Area, Surface Area, and Volume
Problems
Topic A: Area of Triangles, Quadrilaterals, and
Polygons
Lesson 3: The Area of All Triangles
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
altude. 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.

10. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
10
May 27, 2014
Remember in Lesson 1......
How do we find the area of a rectangle?
How do we find the area of a parallelogram?
We needed to find the HEIGHT by making a
right angle with the base...

11. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
11
May 27, 2014
4cm
3cm 3cm
6cm
8cm
10cm
3cm
4cm
It was easy to
find the area of
a right triangle
because the side
was the height.
But what about these??

12. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
12
May 27, 2014
Notice that by drawing the altitude we have created two right triangles.
How can we calculate the area of the entire triangle?
1.
p. 11

13. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
13
May 27, 2014
MODULE 5 Area, Surface Area, and Volume
Problems
Topic A: Area of Triangles, Quadrilaterals, and
Polygons
Lesson 4: The Area of All Triangles
Student Outcomes
§ Students construct the altude for three different cases: an altude that is a side of a right angle, an altude that lies over the base,
and an altude that is outside the triangle.
§ Students deconstruct triangles to jusfy that the area of a triangle is exactly one half the area of a parallelogram.

14. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
14
May 27, 2014
p. 15

15. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
15
May 27, 2014
p. 17

16. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
16
May 27, 2014
p. 17

17. Module 5 Lesson 2­4 Area of All Triangles Combined.notebook
17
May 27, 2014
Closing
Please take out your exit ticket for Lesson 2,3,4, close your
binder, and complete the exit ticket. This will be collected.
§ How are the area formulas of rectangles and right triangles related?
ú Every type of triangle fits inside exactly half of a rectangle that has the
same base and height lengths.
§ When a triangle is not a right triangle, how can you determine its base and
height?
ú The height of a triangle is the length of the altude. The altude is the line
segment from a vertex of a triangle to the line containing the opposite side (or
the base) that is perpendicular to the base.
§ Why does the area formula for a triangle work for every triangle?
ú Every type of triangle fits inside exactly half of a rectangle that has the
same base and height lengths.