Download Lesson 6 - Two-Dimensional Figures

Geometry
Chapter 1
Lesson 1-6
Example 1 Identify Polygons
Name each polygon by its number of sides. Then classify it as convex or concave and regular or
irregular.
a.
b.
Polygon JKLMN has five sides. It is a
pentagon. If ML is extended, it passes
through the interior of the pentagon. So,
the pentagon is concave.
Since it is concave pentagon JKLMN
cannot be regular.
Polygon RSTUVW has six sides, so it is
a hexagon. No lines containing the sides
of the hexagon pass through the interior.
Therefore, the polygon is convex.
Since all sides and all angles are
congruent, hexagon RSTUVW is regular.
Example 2 Find perimeter and area
GARDENING A landscape designer is putting black plastic edging around
a rectangular flower garden that has length 6.4 meters and width 5.7 meters.
The edging is sold in 5-meter lengths.
a. Find the perimeter of the garden and determine
how much edging the designer should buy.
P = 2 + 2w
P = 2(6.4) + 2(5.7)
 = 6.4, w = 5.7
P = 12.8 + 11.4 or 24.2
The perimeter of the garden is 24.2 meters.
The designer needs to buy 25 meters of edging,
or 5 pieces.
b. Suppose the designer needs to know the area of the garden in order to
plan where to place each plant. Find the area of the garden.
A = w
A = (6.4) (5.7)
 = 6.4, w = 5.7
A = 36.48
The area of the garden is 36.48 square meters.
1
Geometry
Chapter 1
Example 3 Test Example
Bill wants to create a rectangular enclosure for his dog out of 84 feet of
fencing. Which of the following shapes will have the greatest area?
A a rectangle with length 26 and width 16
B a rectangle with length 30 and width 12
C a square with length and width of 21
D a rectangle with length 24 and width 18
Read the Test Item
You are asked to compare the areas of four rectangles and choose the one with greatest area.
Solve the Test Item
Find the area of each rectangle.
Rectangle A: A = w
A = (26)(16)
A = 416
Rectangle B: A = w
A = (30)(12)
A = 360
Rectangle C: A = w
A = (21)(21)
A = 441
Rectangle D: A = w
A = (24)(18)
A = 432
Since the square has greatest area, the answer is C
Example 4 Perimeter and Area on the Coordinate Plane
2
Geometry
Chapter 1
COORDINATE GEOMETRY Find the perimeter and area of
triangle ABC if A(2, 7), B(5, 1) and C(-4, 1).
Use the Distance Formula,
d = (x2 - x1)2 + (y2 - y1)2,
to find AB, BC and CA.
AB =
=
(2  5) 2  (7  1) 2
(3) 2  (6) 2
= 45
≈ 6.7
BC =
=
[5  (4)] 2  (1  1) 2
AC =
(9) 2  (0) 2
=
= 81
=9
The perimeter of triangle ABC is
(4  2) 2  (1  7) 2
(6) 2  (6) 2
= 72
≈ 8.5
45 +
72 + 9 or about 24.2 units.
The height of the triangle is the perpendicular distance from A to BC . Counting the squares on
the graph, the height is 6 units. The length of the base, BC , is 9 units.
1
A  bh
2
1
A  (9)(6)
2
A = 27
Area of a triangle
Substitution
Simplify.
The area of triangle ABC is 27 square units.
3