This document presents a math lesson on calculating the area of right triangles. It introduces the formula for finding the area of a right triangle using half the base times the height. Students work through examples calculating areas of various right triangles. They also answer questions about cutting shapes, such as paper and tiles, and determining which shapes have greater areas. The goal is for students to understand and apply the formula for the area of a right triangle.

1. Lesson 2: The Area ofRight Triangles
Date: 5/12/15 S.6
6
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 2
Lesson 2: The Area of Right Triangles
Classwork
Exploratory Challenge
1. Use the shapes labeled with an “x” to predictthe formula needed to calculatethe area of a righttriangle. Explain
your prediction.
Formula for the Area of Right Triangles:______________________________________
Area of the given triangle:_________________________________
2. Use the shapes labeled with a “y” to determine if the formula you discovered in part one is correct.
Does your area formula for triangley match the formula you got for trianglex?
If so, do you believe you have the correctformula needed to calculatethe area of a righttriangle? Why or why not?
If not, which formula do you think is correct? Why?
Area of given triangle:_____________________________________

2. Lesson 2: The Area ofRight Triangles
Date: 5/12/15 S.7
7
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 2
Exercises
Calculatethe area of each trianglebelow. Each figureis not drawn to scale.
3.
4.
5.
6.
15 ft.
8 ft.
17 ft.
17.7 cm
11.4 cm
24.8 cm
8 in.
10 in.
6 in.
5
3
5
m10
1
3
m
8
2
3
m

3. Lesson 2: The Area ofRight Triangles
Date: 5/12/15 S.8
8
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 2
7.
8. Mr. Jones told his students they each need a half of a piece of paper. Calvin cuthis piece of paper horizontally and
Matthew cut his pieceof paper diagonally. Which studenthas the larger area on their half pieceof paper? Explain.
9. Ben took 3 bathroom tiles to the store to be cut. The only direction he gave was that he needed the area of each
tileto be half of the original size. If Ben wants each tileto be cut into two right triangles,did he providethe store
with enough information? Why or why not?
10. If the area of a triangleis 6.22 sq.in.and its baseis 3.11 in.,write an equation that relates the area to the height, ℎ,
and the base. Solve the equation to determine the height.
21.4 km
32.7 km
Calvin’s Paper Matthew’s Paper

4. Lesson 2: The Area ofRight Triangles
Date: 5/12/15 S.9
9
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 2
Problem Set
Calculatethe area of each right trianglebelow. Each figure is not drawn to scale.
1.
2.
3.
4.
9.1 cm
31.2 cm
32.5 cm
3
3
4
km
5 km
6
1
4
km
61 mm
60 mm
11 mm
5 in.
2.4 in.
3.2 in.

5. Lesson 2: The Area ofRight Triangles
Date: 5/12/15 S.10
10
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 2
5.
6. Elania has two congruent rugs at her house. She cut one vertically down the middle, and she cut diagonally through
the other one.
After makingthe cuts, which rug (labeled A, B, C, or D) has the larger area? Explain.
7. Give the dimensions of a righttriangleand a parallelogramwith the same area. Explain howyou know.
8. If the area of a right triangleis
9
16
sq.ft. and the height is
3
4
in.,write an equation that relates the area to the base, 𝑏,
and the height. Solve the equation to determine the base.
16
2
3
ft.
10 ft.
13
1
3
ft.
A B
C
D