Areas%20of%20Polygons%20and%20Circles

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Chapter 11

• Areas of Polygons and Circles

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11.1 Areas of Parallelograms

• The height is always perpendicular to the base

b
A bh
h
l
A lw
w
A s2
s
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11.1 Areas of Parallelograms
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11.1 Areas of Parallelograms
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11.1 Areas of Parallelograms
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11.1 Areas of Parallelograms
Find the area of the figure. Round to the
nearest tenth if necessary.
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11.1 Areas of Parallelograms
Find the height and base of the parallelogram if
the area is 168 square units.
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11.2 Areas of Triangles
h
b
A bh
h
b
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11.2 Areas of Triangles
Find the area of the figure. Round to the
nearest tenth if necessary.
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11.2 Areas of Triangles

• The height of a triangle is 12 inches more than
  its base. The area of the triangle is 560 square
  inches. Find the base and the height.

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11.2 Areas of Trapezoids
b1
A h(b1b2)
h
b2
median
A h x median
h
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11.2 Areas of Trapezoids
Find the area of the trapeziod.
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11.2 Areas of Trapezoids
Find the area
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11.2 Areas of Trapezoids
Trapezoid QRST has an area of 210 square yards.
Find the height of QRST.
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11.2 Areas of Rhombi
A d1d2
d1
d2
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11.2 Areas of Rhombi
Find the area of the rhombus.
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11.2 Areas of Rhombi

• One diagonal of a rhombus is half as long as the
  other diagonal. If the area of the rhombus is 64
  square inches, what are the lengths of the
  diagonals?

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11.3 Areas of Regular Polygons

• Write the formula
• Try to find the Perimeter
• Find the of degrees in the shape
• Divide by the of sides
• Divide by 2
• Use sin-cos-tan to get the apothem
• Substitute and solve

a

A Pa
a

a apothem
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11.3 Areas of Regular Polygons
What is the area of an octagon with an apothem
length of 14 inches? Round to the nearest tenth
if necessary.
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11.3 Areas of Regular Polygons
Find the area of the regular hexagon. Round to
the nearest tenth.
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11.3 Areas of Regular Polygons
Find the area of the regular pentagon. Round to
the nearest tenth.
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11.3 Areas of Circles and Sectors
A ?r2
r
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11.3 Areas of Circles and Sectors
Find the area of the circle.Round to the nearest
tenth.
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11.3 Areas of Circles and Sectors
Find the area of the semi-circle.Round to the
nearest tenth.
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11.3 Areas of Circles and Sectors

• Find the radius of a circle with an area of 58
  square inches.

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11.4 Composite Figures
POOL The dimensions of an irregularly shaped
pool are shown. What is the area of the surface
of the pool?
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11.4 Composite Figures
Find the area of the shaded figure.
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11.4 Composite Figures
Find the area of the figure in square feet. Round
to the nearest tenth if necessary.
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11.4 Composite Figures
Find the area of the figure. Round to the nearest
tenth if necessary.
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11.4 Composite Figures
Find the area of the shaded region. Assume that
the polygon is regular. Round to the nearest
tenth.
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11.4 Composite Figures
Find the area of the shaded region. Assume that
the polygon is regular. Round to the nearest
tenth.
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11.5 Geometric Probability and Areas of Sectors
r
A ?r2
Area of region you want
Probability
Area of whole shape/region
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11.5 Geometric Probability and Areas of Sectors
Find the area of the sector.Round to the nearest
tenth.
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11.5 Geometric Probability and Areas of Sectors

• A pie has a diameter of 9 inches and is cut into
  10 congruent slices. What is the area of one
  slice to the nearest hundredth?

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11.5 Geometric Probability and Areas of Sectors

• A pizza has a diameter of 14 inches and is cut
  into 8 congruent slices. What is the area of one
  slice to the nearest hundredth?