Geometry Chapter 9 – Extending Perimeter, Circumference, and Area
Lesson 1 – Developing Formulas for Triangles and Quadrilaterals
Learning Targets
LT9-1: Solve problems involving the perimeter
and area of triangles and special
quadrilaterals.
Success Criteria
•
•
•
**Refer to the formula sheet for area formulas.
Ex#1: Find measurements of parallelograms.
A. Find the area of the parallelogram.
B. Find the height of a rectangle in which
b = 3 in and A = (6x2 + 24x – 6) in2.
C. Find the perimeter of the rectangle in which
A = (79.8x2 – 42) cm2.
Find measurements of parallelograms.
Find measurements of triangles and
trapezoids.
Find measurements of rhombuses and
kites.
Ex#2: Find measurements of triangles and trapezoids.
A. Find the area of a trapezoid in which b1 = 8in, b2 = 5in, and h = 6.2in.
B. Find the base of the triangle in which A=(15x2)cm2.
C. Find b2 of the trapezoid, in which A = 231mm2.
Ex#3: Find measurements of rhombuses and kites.
A. Find d2 of a kite in which d1 = 14in and A = 238in2.
B. Find the area of the rhombus.
C. Find the area of the kite.
Ex#4: Solve application problems involving the perimeter and area of triangles and special
quadrilaterals.
The tile design shown is a rectangle with a base of 4in and a height of 2in. Use the grid to find the
perimeter and area of the leftmost shaded parallelogram.
Lesson 2 – Developing Formulas for Circles and Regular Polygons
Learning Targets
LT9-2: Apply the formula for the area and
circumference of circles and the area and
Circle:
Center of a Circle:
π
Center of a Regular Polygon
Apothem:
Central Angle of a Regular Polygon:
Ex#1: Find measurements of circles.
A. Find the area of ⊙K in terms of π.
Success Criteria
•
•
Find measurements of circles.
Find the area of a regular polygon.
B. Find the radius of ⊙J if the circumference is (65x + 14)π m.
C. Find the circumference of ⊙M if the area is 25x2 π ft2.
Ex#2: Find the area of a regular polygon.
A. Find the area of a regular heptagon with side
length 2 ft. Round to the nearest tenth.
B. Find the area of a regular hexagon with
apothem 6 cm. Round to the nearest tenth.
Lesson 3 – Composite Figures
Learning Targets
LT9-3: Find the area of
composite figues and
estimate the areas of
irregular shapes.
Success Criteria
•
•
•
•
Find the areas of composite figures by adding.
Find the areas of composite figures by subtracting.
Solve application problems involving composite figures.
Estimate areas of irregular shapes.
Composite Figures:
Ex#1: Find the areas of composite figures by adding. Round to the tenths.
A.
B.
Ex#2: Find the area of composite figures by subtracting. Round to the tenths.
A.
B.
Ex#3: Solve application problems involving composite figures.
A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red.
To dye 6in2 of fabric, 2oz of dye is needed. How much dye is needed for the entire order?
Ex#4: Estimate the areas of irregular shapes.
Use a composite figure to estimate the shaded area.
The grid has squares with a side length of 1ft.
Lesson 4 – Perimeter and Area in the Coordinate Plane
Learning Targets
LT9-4: Find the area and
perimeter of figures in the
coordinate plane.
Success Criteria
•
•
•
Estimate areas of irregular shapes in the coordinate plane.
Find perimeter and area in the coordinate plane.
Find areas in the coordinate plane by subtracting.
In Lesson 9-3, you estimated the area of irregular shapes by drawing composite figures that
approximated the irregular shapes and by using area formulas.
Another method of estimating area is to use a grid and count the squares on the grid.
Ex#1: Estimate areas of irregular shapes in the coordinate plane.
A. Estimate the area of the irregular shape.
B. Estimate the area of the irregular shape.
Ex#2: Find perimeter and area in the coordinate plane.
A. Classify the polygon below.
Find the perimeter and area of the polygon.
B. Classify the polygon below.
Find the perimeter and area of the polygon.
Ex#3: Find areas in the coordinate plane by subtracting.
A.
B.
Lesson 5 – Effects of Changing Dimensions Proportionally
Learning Targets
LT9-5: Describe how transformations
change perimeter and area.
Success Criteria
•
•
•
Describe effects of changing one dimension.
Describe effects of changing dimensions
proportionally.
Describe the effects of changing the area.
Ex#1: Describe the effects on the area of a figure by changing ONE dimension.
A. The height of a triangle is multiplied by 6.
B. The diagonal SU of the kite is multiplied by
⅓.
Ex#2: Describe the effects on the perimeter and area of a figure by changing dimensions
PROPORTIONALLY.
A. The base and height of a rectangle with base
B. The radius of ⊙J is multiplied by ⅕.
4ft and height 5ft are both doubled.
C. The base and height of the triangle with vertices P(2, 5), Q(2, 1), and R(7, 1) are tripled. Describe
the effect on its area and perimeter.
Ex#3: Describe the effects of changing the area.
A. A circle has circumference of 32 π in. If the area is multiplied by 4, what happens to the radius?
B. An equilateral triangle has perimeter of 21m. If the area is multiplied by ½ , what happens to the
side length?
Effects of Changing Dimensions
Change in Dimensions
Perimeter or Circumference
Area
One dimension is multiplied
by “a”
Area is multiplied by a
All dimensions are multiplied by P or C is multiplied by a
“a”
Area is multiplied by a2
Lesson 6 – Geometric Probability
Learning Targets
LT9-6: Calculate geometric probabilities.
Success Criteria
•
•
•
•
Use length to find geometric probability.
Apply geometric probability to real
situations.
Use angle measure to find geometric
probability.
Use area to find geometric probability.
In geometric probability, the probability of an event is based on a ratio of geometric measures such as
length or area. The outcomes of an experiment may be points on a segment or in a plane figure.
Ex#1: Use length to find geometric probability.
A point is chosen randomly on PS . Find the probability of each event.
A. The point is on
RS .
B. The point is not on QR .
C. The point is on
PQ or QR .
Ex#2: Apply geometric probability to real situations.
A pedestrian signal at a crosswalk has the following cycle: WALK for 45 seconds and DONT WALK
for 70 seconds.
A. What is the probability the signal will show WALK when you arrive?
B. If you arrive at the signal 40 times, predict about how many times you will have to stop and wait
more than 40 seconds.
Ex#3: Use angle measure to find geometric probability.
Use the spinner to find the probability of each event.
A. The pointer landing on yellow.
B. The pointer landing on blue or red.
C. The pointer not landing on green.
Ex#4: Use area to find geometric probability.
Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the
hundredth.
A. the circle
B. the trapezoid
C. one of the two squares
Chapter 9 – Perimeter, Circumference, and Area
Homework Assignments
Lesson
Problems
9.1 p. 594
#11-25, 28, 49, 52, 53, 66
9.2 p. 603
#10-23, 26, 28-30, 40, 43, 44, 52, 53
9.3 p. 609
#9-21, 31-33, 39, 40
9.4 p. 620
#10, 13, 14, 16, 19, 24, 25
9.5 p. 625
#8-17, 20, 24-27, 30-33
9.6 p. 634
#16-30, 32, 34-37, 38*