Transcript Lesson 1 Contents

Transparency 11-4
5-Minute Check on Lesson 11-3
Find the area of each regular polygon. Round to the nearest tenth if
necessary.
1. A hexagon with side length 8 cm.
A = 166.3 cm²
2. A square with an apothem length of 14 in.
A = 784 in²
3. A triangle with a side length of 18.6 m.
A = 149.8 m²
Find the area of each shaded region. Assume all polygons
are regular. Round to the nearest tenth if necessary.
4.
5.
A = 51.4 units²
5
6.
Standardized Test Practice:
inches.
A
4π
B
8π
9
A = 92.5 units²
Find the area of a circle with a diameter of 8
C
16π
Click the mouse button or press the
Space Bar to display the answers.
D
64π
Lesson 11-4
Areas of Irregular Figures
Objectives
• Find areas of irregular figures
• Find areas of irregular figures on the
coordinate plane
Area of Irregular Shapes
Irregular Shapes Area:
Sum of Separate Parts
h
r
x
Example Area:
A = ½ circle + triangle + square
A = ½ * πr2 + ½ x * h + x * x
Irregular Shapes Example 1
12
6
12
8
Area of shape = Area of semi-circle + Area of square + Area of triangle
semi-circle area = ½ πr² = ½ π6² = 18π
square area = s² = 12² = 144
triangle area = ½ bh = ½ 12(8) = 48
Area of shape = 18π + 144 + 48 = 192 + 18π = 248.55
Irregular Shapes Example 2
120 yards
30 yds
12
8
Area of shape = 2 Areas of semi-circle + Area of rectangle
2*semi-circle area = 2(½ πr²) = π30² = 900π
rectangle area = l·w = 120·60 = 7200
Area of shape = 900π + 7200 = 10,027.43 square yards
Find the area of the figure in square feet. Round to the nearest
tenth if necessary.
The figure can be separated into a rectangle with dimensions 16
feet by 32 feet, a triangle with a base of 32 feet and a height of
15 feet, and two semicircles with radii of 8 feet.
Area formulas
Substitution
Simplify.
Use a calculator.
Answer:
The area of the irregular figure is 953.1 square feet to
the nearest tenth.
Find the area of the figure in square feet. Round to the nearest
tenth if necessary.
Answer:
A rectangular rose garden is centered in a border of lawn. Find
the area of the lawn around the garden in square feet.
rose garden
The length of the entire lawn is 25 + 100 + 25 or 150 feet.
The width of the entire lawn is 25 + 20 + 25 or 70 feet.
The length of the rose garden is 100 feet and the width is 20 feet.
area of irregular figure = area of entire lawn – area of rose garden
Area formulas
Substitution
Simplify.
Simplify.
Answer:
The area of the lawn around the garden is 8500 sq feet.
INTERIOR DESIGN Cara wants to wallpaper one wall of her
family room. She has a fireplace in the center of the wall. Find
the area of the wall around the fireplace.
Answer:
Find the area of polygon MNPQR.
First, separate the figure into
regions. Draw an auxiliary line
perpendicular to QR from M (we
will call this point S) and an
auxiliary line from N to the xaxis (we will call this point K).
This divides the figure into
triangle MRS, triangle NKM,
trapezoid POKN and trapezoid
PQSO.
Now, find the area of each of the figures.
Find the difference between
x-coordinates to find the lengths of the
bases of the triangles and the lengths of
the bases of the trapezoids.
Find the difference between
y-coordinates to find the heights of the
triangles and trapezoids.


Area
formulas
Substitution
Simplify.
Answer:
The area of polygon MNPQR is 44.5 sq units.
Find the area of polygon ABCDE.
Answer:
Summary & Homework
• Summary:
– The area of an irregular figure is the sum
of the areas of its nonoverlapping parts
• Homework:
– pg 619-621; 3, 8-13