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Hyde Park High School
Teacher Lesson Plan
Grades: 10 & 11
Content: Geometry (Section H3)
Mr. Prospere, Mr. Erilus, Mr. Coriolan
Rationale/Background
For the past two weeks, 10th and 11th grade students
have been studying areas of parallelograms, areas of
triangles, trapezoids and rhombi in their geometry
class.This lesson builds from previous lesson and is
geared toward helping students develop and apply
new geometry concepts.The students have already
mastered certain concepts such as triangle,
quadrilateral, polygon, etc. in this lesson, they will
learn how to find the area of regular polygon, a
concept related to MCAS standards.
Content objectives:
At the end of this lesson, student will be able to:
a) find the area of a regular polygon
b) …altitude of a right triangle and its area formula.
Language Objectives:
At the end of this lesson, student will be able to:
a) describe how to find the area of a regular polygon
b) write and add new terms in their vocabulary builder
worksheets
c) Define orally the theorem: Area of a regular Polygon
Materials:
Paper
Compass
Ruler
Protractor
Straightedge
Textbook:
Glencoe Geometry(Section H3) - Chapter 11-3:areas of
regular Polygons
Startup/Motivation:
• Describe the difference between a regular and
irregular polygon.
Vocabulary
Apothem
Polygon
Irregular Polygon
Congruent Isosceles
Vertex
Radius
Hexagon
Altitude
Building Background Knowledge
Based on the students’ Prior Knowledge, they can define
and recognize the following:
Definition of a regular polygon
Recognizing characteristics of regular polygons
Special Right Triangles (450- 450-900 & 300-600-900)
Define the word apothem to the students
• A regular polygon can be divided into
congruent isosceles triangles by drawing a line
from each vertex to the center of the polygon.
• The altitude of one of these triangles is called
apothem.
• The area of the polygon can be determined by
adding the areas of the triangles.
Strategies
Have students identify from the figure the center
of the circle, the radius of the circle, the
apothem of the polygon and the sides of the
polygon.
Let a represent the length of the apothem and s
represent the length of a side of the hexagon
• since the apothem is perpendicular to a side of
one of the six congruent triangle.
• Ask students how to find the area of the
triangle.
• Have them write the formula
(continued…)
• Area of one of the triangles=1/2bh=1/2sa (s
represents the side and a the apothem)
• Remind students that the triangles are
congruent, therefore they have the same
apothem.
• Have them write the area of all the other
isosceles triangles in the terms of the
apothem a and the length of each side s.
• Have them find the area of the hexagon by
adding up the areas
• Area= 1/2as+1/2as+1/2as+1/2as+1/2as+1/2as
(Continued…)
• =(1/2)(6as)
• =(1/2)(6s) (a)
• since 6s represents the Perimeter(P) of the
hexagon,
• ask students to substitute P for 6s
• Area=(1/2)Pa
• student may use the above expression as a
formula to find the area of a regular n-gon.
• If students have difficulty finding the apothem
of the polygon, explain to them how right
triangle trigonometry may be used.
Key concept: Area of a regular polygon
The area of a regular polygon is half the product of the
apothem and the perimeter.
• Have students express their ideas in writing and
orally
• they get help from their teachers to improve their
language skills.
• Rely on visual learning to assess ELL’s ability to use
inductive reasoning.
• Teacher may define words by using objects in the
classroom as illustration.
• Discuss students’ responses. They may describe the
same pattern in more than one way
(continued…)
• Use of index cards to illustrate key concepts
• Have students use cooperative learning. They take
turns with their partners to explain a concept in their
own words and teacher makes correction
• Have students practice reading in their math
textbooks
• English language learners may be unfamiliar with
some words, teacher helps them break them into its
prefix and its root scribe or if necessary, use
students’ native language for better meaning and
understanding.
Ongoing assessment
• Have students make connection by taking them
outside to observe and record real-world examples
related to the lesson.
• Connecting to prior knowledge
• Have students choose a partner and have them draw
a regular polygon (a square for example) with the
radius of the circumscribed circle . Then ask them to
use the area formula to calculate the area by first
finding the apothem.
• Have student work through examples and exercises in
their math textbook.
(Continued…)
• Encourage them to apply definitions, concepts,and
theorems they have learned to solve problems.
• Have them summarized the main ideas of the lesson in
writing and verbally.
• Ask them to add the new vocabulary terms to their
previous vocabulary list.
Practice/Application
1) Find the area of an equilateral triangle with apothem 6 inches.
2) Find the area of a square with radius 4 centimeters.
3) Find the area of a regular hexagon with side length 12 feet.
Homework assignment:
Chapter 11 unit 3: practice and apply, page 613 exercises 10-20 even
numbers.