Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

Lesson 8.2. Perimeter and Area of Composite Figures

Math ISU
by

Goppikka Nat

on 1 April 2014

Report abuse

Transcript of Lesson 8.2. Perimeter and Area of Composite Figures

Perimeter and Area
Lesson 8.2
In this section,
Key Concepts:
- To determine the total
of a composite figure, add and/or subtract areas.
To determine the
of a composite figure, add the distances around the outside of the figure.
You will apply
the formulas
for the perimeter
and area of simple
shapes to more
complex shapes.
- A composite figure is made up of
more than one simple shape.
1. Find the area of A1.
2. Find the area of A2.
perimeter
of Composite Figures
This composite figure is
and a rectangle
area
e.g.
How can you apply
and area to a
composite figure?
Example 1:
Area and Perimeter of a Composite Figure
24cm
12cm
4cm
16cm
a) Determine the area of
the trapezoid shown.
b) Determine the perimeter.
Round to the nearest centimetre.
Solution:
a) The trapezoid can be split into a rectangle and two right triangles.
24cm
12cm
4cm
16cm
Understand the Problem
Choose a Strategy
To find the total area of the trapezoid, add the area of the rectangle and the areas of the two right triangles. Use the formulas for the areas of these shapes.
Area of rectangle: length x width
Area of triangle: base x height / 2
Formulas
Carry Out the Strategy
Call the area of
the rectangle: AR
AR = lw
= (24)(16)
= 384

AT1 = ½ bh
= ½ (12)(16)
= 96

AT2 = ½ bh
= ½ (4)(16)
= 32
Call the area of
the triangle on
the left: AT1
Call the area of
the triangle on
the right: AT2
Call the total area: Atotal
Atotal = AR + AT1 + AT2
= 384 + 96 + 32
= 512
The total area of the
trapezoid is 512cm2.
Conclusion:
b) The perimeter of the
trapezoid includes two unknown side lengths.
When the figure is split into a rectangle
and two right triangles, each unknown side is in a triangle. Apply the Pythagorean theorem to determine the lengths of the two unknown sides in the perimeter.
Understand the Problem
Choose a Strategy
24cm
12cm
4cm
16cm
In both triangles,
the unknown side
is the hypotenuse.
First, find the length of the unknown side on the left.
Call it; c. The length of
c = 20cm.
c² = a² + b²
= 12² + 16²
= 144 + 256
= 400
c = √400
= 20
Next, find the length of the unknown side on the right. Call it d. The length of d = 16cm.
d² = a² + b²
= 4² + 16²
= 16 + 256
= 272
d = √272
= 16
Now, find the perimeter by adding the outside measurements.
P = 24 + 16 + 40 + 20
= 100
The perimeter of
the trapezoid is
approximately 100cm.
Carry Out the Strategy
Conclusion:
Example 2:
Area of a Composite Figure,
by Subtraction, and Perimeter
a) Describe the steps you would use to find the area of the walkway.
b) Calculate the area of the walkway. Round to the nearest tenth of a square metre.
c) The walkway will have a border in a different colour of tile. Calculate the perimeter of the walkway. Round to the nearest tenth of a metre,
A hotel is remodelling its outdoor entrance area.
2.1m
5.2m
Solution:
a) The walkway is a rectangle with a semicircle cut out of it.
Determine the area of the rectangle minus the area of the semicircle.
5.2m
2.1m
b)
AR = lw
= (5.2)(2.1)
= 10.92
Call the area of the rectangle: AR
Call the area of the semicircle: AS
AS = ½ π r ²
= ½ π (1.05) ²
= 1.73
Call the total area of the walkway: AW
AW = AR - AS
= 10.92 - 1.73
= 9.19
The total area of
the walkway is approximately 9.2m²
c) The perimeter of the walkway consists of the three sides of the rectangular section and
the semicircular arc.
First, find the length of the semicircular arc.
L = ½ (πd)
= ½ π(2.1)
= 3.3
Now, add the distances around the outside of the walkway.
Pwalkway = L + 3 sides of rectangle
= 3.3 + (5.2 + 2.1 + 5.2)
= 15.8
Conclusion:
The perimeter of the