1. Polygons, Circles, and Solids
Section 2.3
Polygons, Circles, and Solids

2. Common Polygons

3. Triangles

4. Quadrilaterals

5. Sum of Interior angles of Regular Polygon
Interior sum of angles of regular polygon is
(n-2)180, n is the number of sides
What is the measure of the interior angles of a STOP sign?
1080 degree.

6. A rectangle has four sides that meet to form 90° angles
A rectangle has four sides that meet to form 90° angles. Each set of opposite sides is parallel and congruent (has the same length).
90°
angles
In a rectangle, if one
right angle is shown,
the other three are
also right angles.
5 cm
9 cm
Each longer side of a rectangle is
called the length (l) and each
shorter side is called the width (w).
Slide

7. Slide

8. Finding the Perimeter of a Rectangle
Parallel
Example 1
Finding the Perimeter of a Rectangle
Find the perimeter of each rectangle. a.
6 m
16 m
P = 2 • l • w
P = 2 • 16 m • 6 m
P = m m
P = 44 m
The perimeter of the rectangle is 44 m.
Slide

9. Finding the Perimeter of a Rectangle
Parallel
Example 1
continued
Finding the Perimeter of a Rectangle
Find the perimeter of each rectangle.
b. A rectangle 7.8 ft by 12.3 ft
P = 2 • l • w
P = 2 • 12.3 ft • 7.8 ft
P = ft ft
P = ft
Or, you can add up the lengths of the four sides.
P = ft ft ft ft
P = ft
Either method will give you the same result.
Slide

10. The perimeter of a rectangle is the distance around the outside edges.
The area of a rectangle is the amount of surface
inside the rectangle.
1 m
1 square meter or
(m)2
8 m
5 m
We have five rows of eight
square meters for a total of
40 square meters.
Slide

11. Slide

12. Other sizes of squares that are often used to measure area:
Squares of many sizes can be used to measure area. For smaller areas, you might use the ones shown below.
(Approximate-size drawings)
1 square inch
(1 in.2)
1 in.
1 square
centimeter
(1 cm2)
1 cm
1 square
millimeter
(1 mm2)
1 mm
Other sizes of squares that are often used to measure area:
1 square meter (1 m2)
1 square foot (1 ft2)
1 square kilometer (1 km2)
1 square yard (1 yd2)
1 square mile (1 mi2)
Slide

13. Finding the Area of a Rectangle
Parallel
Example 2
Finding the Area of a Rectangle
Find the area of each rectangle. a.
7 yd
15 yd
A = l • w
A = 15 yd • 7 yd
A = 105 yd2
Slide

14. Finding the Area of a Rectangle
Parallel
Example 2
continued
Finding the Area of a Rectangle
Find the area of each rectangle. b.
18 cm
3 cm
A = l • w
A = 18 cm • 3 cm
A = 54 cm2
Slide

15. Slide

16. Finding the Perimeter and Area of a Square
Parallel
Example 3
Finding the Perimeter and Area of a Square
a. Find the perimeter of a square where each side measures 7 m.
Use the formula.
Or add up the four sides.
P = 4 • s
P = 7 m + 7 m + 7 m + 7 m
P = 4 • 7 m
P = 28 m
P = 28 m
Same answer
Slide

17. Finding the Perimeter and Area of a Square
Parallel
Example 3
continued
Finding the Perimeter and Area of a Square
b. Find the area of a square where each side measures 7 m.
A = s2
A = s • s
A = 7 m • 7 m
A = 49 m2
Square units for area.
Slide

18. Finding the Perimeter and Area of a Composite Figure
Parallel
Example 4
Finding the Perimeter and Area of a Composite Figure
a. The floor of a room has the shape shown.
6 ft
30 ft
21 ft
24 ft
15 ft
Suppose you want to put new wallpaper border along the top of the walls. How much material do you need?
Find the perimeter of the room by adding up the length
of the sides.
P = 30 ft + 21 ft + 24 ft + 15 ft + 6 ft + 6 ft
= 102 ft
Slide

19. Finding the Perimeter and Area of a Composite Figure
Parallel
Example 4
continued
Finding the Perimeter and Area of a Composite Figure
b. The carpet you like cost $24.25 per square feet. How much will it cost to carpet the room?
6 ft
30 ft
21 ft
24 ft
15 ft
Slide

20. Finding the Perimeter and Area of a Composite Figure
Parallel
Example 4
continued
Finding the Perimeter and Area of a Composite Figure
Finally, multiply to find the cost of the carpet.
36+504= 540 sq feet.
6 ft
21 ft
24 ft
Slide

21. A parallelogram is a four-sided figure with opposite sides parallel, such as the ones below. Notice that the opposite sides have the same length.
Slide

22. Finding the Perimeter of a Parallelogram
Example 1
Finding the Perimeter of a Parallelogram
Find the perimeter of a the parallelogram.
15 cm
9 cm
P = 15 cm + 9 cm + 15 cm + 9 cm
= 48 cm
Slide

23. Slide

24. Finding the Area of a Parallelogram
Example 2
Finding the Area of a Parallelogram
Find the area of the parallelogram.
10 m
4 m
3 m
4 m
10 m
The base is 10 m and the height is 3 m. Use the formula to solve.
A = b ∙ h
A = 10 m ∙ 3 m
A = 30 m2
Slide

25. A triangle is a figure with exactly three sides
A triangle is a figure with exactly three sides. To find the perimeter of a triangle, add the lengths of the three sides.

26. Finding the Perimeter of a Triangle
Parallel
Example 1
Finding the Perimeter of a Triangle
Find the perimeter of the triangle.
P = 12 ft + 16 ft + 20 ft
= 48 ft
20 ft
12 ft
16 ft

27. Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2 it only works on Right Triangles.
Where a and b are legs and c is the hypotenuse.

28. The height of a triangle is the distance from one vertex of the triangle to the opposite side (base). The height line must be perpendicular to the base; that is, it must form a right angle with the base.

30. Find the Area of a Triangle
Parallel
Example 2
Find the Area of a Triangle
Find the area of each triangle. a.

31. Find the Area of a Triangle
Parallel
Example 2
continued
Find the Area of a Triangle
Find the area of each triangle. c.

32. r d
Slide

33. Finding the Diameter and Radius of a Circle
Parallel
Example 1
Finding the Diameter and Radius of a Circle
Find the unknown length of the diameter or radius in each circle. a.
Because the radius is 12 in.,
the diameter is twice as long.
r = 12 in.
d = ?
d = 2 • r
d = 2 • 12 in.
d = 24 in.
Slide

34. Finding the Diameter and Radius of a Circle
Parallel
Example 1
continued
Finding the Diameter and Radius of a Circle
Find the unknown length of the diameter or radius in each circle. b.
The radius is half the diameter.
r = d 2
r = ?
d = 7 m
r =
7 m 2 1 2
r = 3.5 m or m
Slide

35. The perimeter of a circle is called its circumference.
Circumference is the distance around the edge of a
circle.
Slide

36. Dividing the circumference of any circle by its diameter
always gives an answer close to 3.14.
This means that going around the edge of any circle
is a little more than 3 times as far as going straight
across the circle.
This ratio of circumference to diameter is called
Slide

37. Slide

38. Finding the Circumference of Circles
Parallel
Example 2
Finding the Circumference of Circles
Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth. a.
The diameter is 24 m, so use
the formula with d in it.
24 m
C = • d
C = • m
C ≈ m Rounded
Slide

39. Finding the Circumference of Circles
Parallel
Example 2
Finding the Circumference of Circles
Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth.
In this example, the radius is labeled,
so it is easier to use the formula with
r in it. b.
6.5 cm
C = 2 • • r
C = 2 • • 6.5 cm
C ≈ cm Rounded
Slide

40. Slide

41. Finding the Area of Circles
Parallel
Example 3
Finding the Area of Circles
Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. a.
A circle with a radius of 14.2 cm.
A = • r • r
A ≈ • 14.2 cm • 14.2 cm
A ≈ cm2
Rounded;
square units for area
Slide

42. Finding the Area of Circles
Parallel
Example 3
continued
Finding the Area of Circles
Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. b.
24 ft
First find the radius.
r = d 2
r = = 12 ft
24 ft 2
Now find the area.
A ≈ • 12 ft • 12 ft
A ≈ ft2
Slide

43. HW section 2.3
13-59