1. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
People work with areas in many occupations:
Carpenters calculate the areas of walls, floors, and roofs before they purchase materials for construction.
Painters calculate surface areas so that they know how much paint to buy for a job.
Decorators calculate the areas of floors and windows to know how much carpeting and drapery they will need.
OBJECTIVE:
In this chapter you will discover formulas for finding the areas of the regions within:
triangles
parallelograms
trapezoids
kites
regular polygons, and circles.
JRLeon Geometry Chapter HGSH

2. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
The area of a plane figure is the measure of the region enclosed by the figure.
You measure the area of a figure by counting the number of square units that you can arrange to fill the figure completely.
RECTANGLE:
Any side of a rectangle can be
called a base. A rectangle’s height
is the length of the side that is
perpendicular to the base. For each
pair of parallel bases, there is a
corresponding height.
If we call the bottom side of each rectangle in the figure the base, then the length of the base is the number of squares in each row and the height is the number of rows.
JRLeon Geometry Chapter HGSH

3. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
EXAMPLE A:
Find the area of this shape.
3x2/2
5x2/2
2x3/2
6x3/2
3x2
5x2
2x3
6x3
8x4
3𝑥 𝑥 𝑥 𝑥 𝑥4
= 52
JRLeon Geometry Chapter HGSH

4. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
Parallelogram
Just as with a rectangle, any side of a parallelogram can be called a base. But the height of a parallelogram is not necessarily the length of a side. An altitude is any segment from one side of a parallelogram perpendicular to a line through the opposite side. The length of the altitude is the height.
The altitude can be inside or outside the
parallelogram. No matter where you
draw the altitude to a base, its height
should be the same, because the
opposite sides are parallel.
JRLeon Geometry Chapter HGSH

5. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
Area Formula for Parallelograms h s b
JRLeon Geometry Chapter HGSH

6. Areas of Rectangles and
Lesson 8.1
Areas of Rectangles and
Parallelograms
Area Formula for Parallelograms
EXAMPLE B:
Find the height of a parallelogram that has area 7.13 m2 and base length 2.3 m.
A = bh
A/b = h
7.13/2.3 = h
3.1 m = h
JRLeon Geometry Chapter HGSH

7. JRLeon Geometry Chapter 8.2 HGSH
Lesson 8.2
Areas of Triangles,
Trapezoids, and Kites h b1 b2
b = b1 + b2
Rectangle A1 = b1h
Triangle A1 = b1h/2
Rectangle A2 = b2h
Triangle A2 = b2h/2 (half the rectangle)
Triangle A1 + A2 = b1h/2 + b2h/2
A = (b1 + b2)h/2
= bh/2
JRLeon Geometry Chapter HGSH

8. JRLeon Geometry Chapter 8.2 HGSH
Lesson 8.2
Areas of Triangles,
Trapezoids, and Kites
Area Formula for Trapezoids b2 b1 b2
Area of Parallelogram = bh
= (b1+b2)h h b1
And dividing by 2,
Therefore, the area of the Trapezoid is;
= (b1+b2)h/2
JRLeon Geometry Chapter HGSH

9. JRLeon Geometry Chapter 8.2 HGSH
Lesson 8.2
Areas of Triangles,
Trapezoids, and Kites
Area Formula for Kites d1
d2 𝟐 d2 d1
Area of Rectangle = bh
Area of the Kite = d1d2 𝟐
JRLeon Geometry Chapter HGSH

10. JRLeon Geometry Chapter 8.1-8.2 HGSH
Lesson 8.2
Areas of Triangles,
Trapezoids, and Kites
Class Work / Home Work:
8.1 Pages 425 – 427 : problems 1 thru 17 ODD and 21, 23
8.2 Pages 430 – 432 : problems 1 thru 21 ODD
JRLeon Geometry Chapter HGSH