Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane Figures Seatwork Content Text Pages 434 -437 Below is a study guide that you can use for this unit. Memorize the shapes and their names below. Practice each night so by the end of the unit these and other terms would be easy to remember. 1 1
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Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane FiguresSeatwork Content Text Pages 434 -437
Below is a study guide that you can use for this unit. Memorize the shapes and their names below. Practice each night so by the end of the unit these and other terms would be easy to remember.
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Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane FiguresSeatwork Content Text Pages 434 -437
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Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane FiguresHomework Content Text Pages 434 -437
Below is a study guide that you can use for this unit. Memorize the shapes and their names below. Practice each night so by the end of the unit these and other terms would be easy to remember.
The following figure is not a polygon as it is not a closed figure.
Chapter 8 – Geometry- Lesson 8-14 AREA of CirclesContent Name: ________________________________________
Find the area of the following circles
1. 2.
3. 4.
26
26
18 cm3.4 cm
2 cm
4 cm
1.4 cm 8 cm
5. 6.
Chapter 8 – Geometry- Lesson 8-13 Extra Circumference of CirclesContent Name: ________________________________________
Exercise
1. A circular pond has a diameter of 3.2 m.
a) What is the area of the pond?
b) What is the circumference?
2. A baseball stadium has a circular patch with a radius of 100 metres.
a) The groundsman is going to use a fertilizer and needs to know the area of the pitch. What is the area?
b) He also needs to know what the distance is all
27
27
18 cm3.4 cm
the way round. What is this dimension called and what is its value?
3. The diameter of the Earth at the equator is rather difficult to measure – we would need to dig a very long tunnel!! It is much easier to measure the circumference. The circumference of the Earth is 40,000 km. Can you calculate its diameter?
You could use a calculator and trial and improvement but make a note of each trial and the result.
For each of the following shapes find: a) the perimeter or circumferenceb) the area
A window frame in the shape of a rectangle is 90 centimeters long and 40 centimeters wide What is the perimeter of the window frame?
30
30
A = _______P =
A = _______P =
A = _______P =
A = _______P =
A = _______P =
What is the area of the shaded part of the floor?
Find the Area of the following figures
1.____________
2.____________
3. ____________
4.____________
31
31
5.____________
Tutorials
The area of a composite shape is calculated by splitting the shape into separate shapes. The area of each one is then calculated and the areas are added together to find the total area. In examples below the shapes have been divided into two shapes.
Example 1
Area of shape A = 6 × 4 = 24 cm2
B = 3 × 2 = 6 cm2
Total Area = 24 + 6
= 30 cm2
Example 2
Area of shape C = (5 × 4) = 10 cm2
D = 4 × 3 = 12 cm2
Total Area = 10 + 12
32
32
3 cm
C
D
4 cm
A
B
7 cm
4 cm
6 cm
4 cm
5 cm
= 22 cm2
The distance around the edge of a circle has a special name. It is called the circumference.The circumference is just like the perimeter but is only used when talking about circles.If you know the radius or the diameter of a circle you can calculate its circumference.
The circumference is given by:
C = 2 π r π is a special number and
is always 3.14Example 1
C = 2 π rC = 2 × 3.14 × 5Circumference = 31.4 cm
Example 2
Firstly we need to find the radiusThe radius is half the length of the diameter
r =
r = 3 cm
So C = 2 π rC = 2 × 3.14 × 3
= 18.84 cm
33
33
Area of a circle
5 cm
Circumference of a circle
6 cm
The area of a circle is given by
Area = π × (radius) 2
A = π r 2
Example
Area = π r 2
= π × 52
= 3.14 × 25
= 78.5 cm2
Remember that area always has square units. In this case since the radius is in cm, the area is in square centimetres (cm2)
34
34
5 cm
In a parallelogram the opposite sides are parallel.