Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Find the area of the following
figures. 1. a triangle with a base of 12.4 m and
a height of 5 m 2. a parallelogram with a base
of 36 in. and a height of 15 in. 3. a square
with side lengths of 2.5 yd
31 m2
540 in2
6.25 yd2
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Vocabulary
composite figure
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A composite figure is made up of simple geometric
shapes, such as triangles and rectangles. You can
find the area of composite and other irregular
figures by separating them into non-overlapping
familiar figures. The sum of the areas of these
figures is the area of the entire figure. You can
also estimate the area of irregular figures by
using graph paper.
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Teacher Example 1 Estimating the Area of an
Irregular Figure Estimate the area of the figure.
Each square represents one square yard.
Count the number of filled or almost-filled
squares 47 squares.
Count the number of squares that are about
half-full 9 squares.
Add the number of filled squares plus ½ the
number of half-filled squares 47 ( 9)
47 4.5 51.5
1 2
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Student Practice 1 Estimate the area of the
figure. Each square represents 1 yd2.
Count the number of filled or almost-filled
squares 11 red squares.
Count the number of squares that are about
half-full 8 green squares.
Add the number of filled squares plus ½ the
number of half-filled squares 11 ( 8)
11 4 15.
1 2
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Teacher Example 2 Finding the Area of a
Composite Figure Find the area of the composite
figure. Use 3.14 as an estimate for p.
16 m
9 m
16 m
Use the formula for the area of a parallelogram.
Substitute 16 for b.
Substitute 9 for h.
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Teacher Example 2 Continued Find the area of the
composite figure. Use 3.14 as an estimate for p.
The area of a semicircle is the area of a
circle.
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Substitute 3.14 for p and 8 for r.
Multiply.
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Teacher Example 2 Continued Find the area of the
composite figure. Use 3.14 as an estimate for p.
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Student Practice 2 Find the area of the
composite figure.
9 yd
2 yd
8 yd
Use the formula for the area of a rectangle.
Substitute 8 for l.
Substitute 9 for w.
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Student Practice 2 Continued Find the area of
the composite figure.
9 yd
Substitute 2 for b and 9 for h.
2 yd
8 yd
Multiply.
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Student Practice 2 Continued Find the area of
the composite figure. Use 3.14 as an estimate for
p.
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Teacher Example 3 Problem Solving
Application The Wrights want to tile their entry
with one-square-foot tiles. How much tile will
they need?
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Teacher Example 3 Continued
Rewrite the question as a statement. Find the
amount of tile needed to cover the entry
floor. List the important information The
floor of the entry is a composite figure. The
amount of tile needed is equal to the area of the
floor.
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Teacher Example 3 Continued
Find the area of the floor by separating the
figure into familiar figures a rectangle and a
trapezoid. Then add the areas of the rectangle
and trapezoid to find the total area.
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Teacher Example 3 Continued
Find the area of each smaller figure.
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Teacher Example 3 Continued
Look Back
The area of the entry must be greater than the
area of the rectangle (40 ft2), so the answer is
reasonable.
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Student Practice 3 The Franklins want to
wallpaper the wall of their daughters loft. How
much wallpaper will they need?
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Student Practice 3 Continued
Rewrite the question as a statement. Find the
amount of wallpaper needed to cover the loft
wall. List the important information The
wall of the loft is a composite figure. The
amount of wallpaper needed is equal to the area
of the wall.
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Student Practice 3 Continued
Find the area of the wall by separating the
figure into familiar figures a rectangle and a
triangle. Then add the areas of the rectangle and
triangle to find the total area.
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Student Practice 3 Continued
Find the area of each smaller figure.
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Student Practice 3 Continued
Look Back
The area of the wall must be greater than the
area of the rectangle (108 ft2), so the answer is
reasonable.
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Lesson Quiz
Find the perimeter and area of each figure. 1.
2.
6 cm
8 cm
10 ft
8.1 ft
7 ft
14 ft