geometry composite figures
DESCRIPTION
Geometry Composite Figures. Warm up. Find the area of each regular polygon. Round to the nearest tenth: 1) An equilateral triangle with a side length of 3 cm. 2) A regular hexagon with an apothem of 4√3 m. Composite Figures. - PowerPoint PPT PresentationTRANSCRIPT
CONFIDENTIAL 1
Geometry
Composite Figures
CONFIDENTIAL 2
Warm up
Find the area of each regular polygon. Round to the nearest tenth:
1) An equilateral triangle with a side length of 3 cm.
2) A regular hexagon with an apothem of 4√3 m.
CONFIDENTIAL 3
A composite figure is made up of simple shapes such as triangles, rectangles,
trapezoids and circles. To find the area of a composite figure, find the areas of the simple
shapes and then use the Area Addition Postulate.
Composite Figures
CONFIDENTIAL 4
Divide the figure into rectangles.
Area of top rectangle:A = bh = 12(15) = 180 cm2
Area of bottom rectangle:A = bh = 9(27) = 243 cm2
Shaded area:180 cm2 + 243 cm2 = 423 cm2
Finding the area of Composite Figures by Adding
15 cm
12
cm
21
cm
27 cm
15 cm
12
cm12 cm
27 cm9 cm
A) Find the area of the shaded region.
CONFIDENTIAL 5
Divide the figure into parts.
The base of the triangle is :√(10.22 - 4.82) = 9 ft
Area of triangle:A = 1bh = 1(9)(4.8) = 21.6 ft2
2 2Area of rectangle:A = bh = 9(3) = 27 ft2
Area of half circle:A = 1∏r2 = 1∏(4.52) = 10.125∏ ft2
2 2Shaded area:21.6 + 27 + 10.125∏ ≈ 80.4 ft2
Finding the area of Composite Figures by Adding
B)
10.2 ft
7.8 ft
3 ft
10.2 ft
7.8 ft
3 ft
4.5 ft
CONFIDENTIAL 6
Now you try!
1) Find the area of the given figure. Round to the nearest tenth.
37.5 m
22.5 m
75 m
62.5 m
CONFIDENTIAL 7
Sometimes you need to subtract to find the area of composite figures.
CONFIDENTIAL 8
Finding the area of Composite Figures by Subtracting
Subtract the area of the triangle from the area of the rectangle.
Area of top rectangle:A = bh = 18(36) = 648 m2
Area of triangle:A = 1bh = 1(36)(9) = 162 m2
2 2
Area of the figure:A = 648 – 162 = 486 m2
A) Find the area of the shaded region.
9 m
18 m
36 m
CONFIDENTIAL 9
The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle.
Area of top rectangle:A = bh = 33(16) = 528 ft2
Area of circle:A = ∏r2 = ∏(82) = 64∏ ft2
Area of the figure:A = 528 – 64∏ = 326.9 ft2
B) Find the area of the shaded region.
16 ft
33 ft
CONFIDENTIAL 10
Now you try!
2) Find the area of the shaded region. Round to the nearest tenth.
6 in
CONFIDENTIAL 11
Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the
garden require in one year?
12 ft
28.5 ft
10.5 ft7
.5 f
t
6 f
t
18 ft
19
.5 ft
12 ft
28.5 ft
10.5 ft
7.5
ft
6 f
t
18 ft
19
.5 ft
Divide the garden into parts.Area of top rectangle:A = bh = 28.5(7.5) = 213.75 ft2
Area of center trapezoid:A = 1(12 + 18)(6) = 90 ft2
2Area of bottom rectangle:A = bh = 12(6) = 72 ft2
Area of the garden is:213.75 + 90 + 72 = 375.75 ft2
The garden will use (375.75)(17) = 6387.75 gallons of water per year
CONFIDENTIAL 12
Now you try!
3) The lawn that Katie is replacing requires 79 gallons of water per square foot per year. How much water will
Katie save by planting the xeriscape garden?
12 ft
28.5 ft
10.5 ft
7.5
ft
6 f
t18 ft
19
.5 ft
CONFIDENTIAL 13
To estimate the area of an irregular shape, you can sometimes use a composite figure. First draw a composite figure that resembles the irregular shape. Then divide the composite
figure into simple shapes.
CONFIDENTIAL 14
Estimating areas of irregular shapesUse a composite figure to estimate the shaded area. The grid
gas squares with side length of 1 cm.
Draw a composite figure that approximates the irregular shape. Find the area of each part of the
composite figure.
a
b
c
d
Area of triangle, a:
A = 1bh = 1(3)(1) = 1.5 cm2
2 2
Area of Parallelogram, b:
A = bh = 3(1) = 3 cm2
CONFIDENTIAL 15
Area of trapezoid, c:
A = 1(3 + 2)(1) = 2.5 cm2
2
Area of triangle, d:
A = 1bh = 1(2)(1) = 1 cm2
2 2
Area of composite figure:1.5 + 3 + 2.5 + 1 = 8 cm2
a
b
c
d
The shaded area is about 375.75 ft2
CONFIDENTIAL 16
Now you try!
4) Use a composite figure to estimate the shaded area. The grid gas squares with side length of 1 ft.
CONFIDENTIAL 17
Now some problems for you to practice !
CONFIDENTIAL 18
Find the area of the shaded region. Round to the nearest tenth:
Assessment
1)
2)4
cm
12 cm
5 cm 3 cm 2 cm
4 ft
5 f
t
CONFIDENTIAL 19
3)
4)
8 in
.
18 in.
3 in.
3 m 2 m
6 m
5 m
CONFIDENTIAL 20
5)
Find the area of the shaded region. Round to the nearest tenth:
12 ft
4 ft
12 ft
16 ft6)
12 cm
12
cm
12 cm
CONFIDENTIAL 21
7) Shelby is planting grass in an irregularly shaped garden as shown The grid has squares of side 1 yd. Estimate the area of the garden. Given that grass cost $6.50 per square yard, find the cost of the grass.
CONFIDENTIAL 22
A composite figure is made up of simple shapes such as triangles, rectangles,
trapezoids and circles. To find the area of a composite figure, find the areas of the simple
shapes and then use the Area Addition Postulate.
Composite Figures
Let’s review
CONFIDENTIAL 23
Divide the figure into rectangles.
Area of top rectangle:A = bh = 12(15) = 180 cm2
Area of bottom rectangle:A = bh = 9(27) = 243 cm2
Shaded area:180 cm2 + 243 cm2 = 423 cm2
Finding the area of Composite Figures by Adding
15 cm
12
cm
21
cm
27 cm
15 cm
12
cm12 cm
27 cm9 cm
A) Find the area of the shaded region.
CONFIDENTIAL 24
The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle.
Area of top rectangle:A = bh = 33(16) = 528 ft2
Area of circle:A = ∏r2 = ∏(82) = 64∏ ft2
Area of the figure:A = 528 – 64∏ = 326.9 ft2
B) Find the area of the shaded region.
16 ft
33 ft
CONFIDENTIAL 25
Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the
garden require in one year?
12 ft
28.5 ft
10.5 ft7
.5 f
t
6 f
t
18 ft
19
.5 ft
12 ft
28.5 ft
10.5 ft
7.5
ft
6 f
t
18 ft
19
.5 ft
Divide the garden into parts.Area of top rectangle:A = bh = 28.5(7.5) = 213.75 ft2
Area of center trapezoid:A = 1(12 + 18)(6) = 90 ft2
2Area of bottom rectangle:A = bh = 12(6) = 72 ft2
Area of the garden is:213.75 + 90 + 72 = 375.75 ft2
The garden will use (375.75)(17) = 6387.75 gallons of water per year
CONFIDENTIAL 26
Estimating areas of irregular shapesUse a composite figure to estimate the shaded area. The grid
gas squares with side length of 1 cm.
Draw a composite figure that approximates the irregular shape. Find the area of each part of the
composite figure.
a
b
c
d
Area of triangle, a:
A = 1bh = 1(3)(1) = 1.5 cm2
2 2
Area of Parallelogram, b:
A = bh = 3(1) = 3 cm2
CONFIDENTIAL 27
Area of trapezoid, c:
A = 1(3 + 2)(1) = 2.5 cm2
2
Area of triangle, d:
A = 1bh = 1(2)(1) = 1 cm2
2 2
Area of composite figure:1.5 + 3 + 2.5 + 1 = 8 cm2
a
b
c
d
The shaded area is about 375.75 ft2
CONFIDENTIAL 28
You did a You did a great great job today!job today!