1. Area & Perimeter

2. Objectives: Essential Question: Area & Perimeter
Develop fluency in the use of formulas to solve problems.
Essential Question:
How can I use formulas to find the perimeter and area of simple geometric figures?

3. Vocabulary: Area & Perimeter
Polygon: a closed plane figure bounded by three or more line segments.
Quadrilateral: any four sided polygon.
Parallelogram: a quadrilateral whose opposite sides are parallel.
Square: a four sided polygon characterized by four right angles and four sides of equal length.
Rectangle: a four sided polygon characterized by four right angles and opposite sides of equal measure.
Triangle: a three sided polygon.
Circle: a closed plane curve consisting of all points at a given distance from a point within it called the center.

4. Polygons: Area & Perimeter What do they look like…
A regular polygon is a any polygon in which all sides and angles are congruent.
An irregular polygon is a polygon whose sides are not all the same length and/or whose interior angles do not all have the same measure.

5. Polygons: Area & Perimeter
The following are some examples of regular polygons:

6. Triangles: Area & Perimeter
First lets focus on Triangles since they represent the smallest polygon:
triangles

7. Triangles: Area & Perimeter A = ½bh height (h) height (h) base (b)
The height is the shortest distance from a base to the opposite vertex
height (h)
height (h)
base (b)
base (b)
The base of a triangle can be any one of its sides
A = ½bh

8. A = ½bh A = ½(8)(5) A = 20 sq cm Example 1: Triangles Area & Perimeter
Find the area of the triangle.
A = ½bh
A = ½(8)(5)
A = 20 sq cm

9. A = ½bh A = ½(15)(3) A = 42.5 sq ft Example 2: Triangles
Area & Perimeter
Example 2: Triangles
Find the area of the triangle.
A = ½bh
A = ½(15)(3)
A = 42.5 sq ft

10. A = ½bh A = ½(15.5)(4.4) A = 31.4 sq mm Example 3: Triangles
Area & Perimeter
Example 3: Triangles
Find the area of the triangle.
A = ½bh
A = ½(15.5)(4.4)
A = 31.4 sq mm

11. Analyzing Quadrilaterals:
Area & Perimeter
Analyzing Quadrilaterals:

12. Quadrilaterals: Area & Perimeter
Now lets focus on some important kinds of Quadrilaterals:
Square
Rectangle
Parallelogram
Trapezoid

13. Squares: Area & Perimeter A = lw = bh Side Parallel sides Side

14. Example 4: Squares P = 4s P = 4 · 4 P = 16 sq in A = s2 A = 42
Area & Perimeter
Example 4: Squares
Find the perimeter and area of the square.
P = 4s
P = 4 · 4
P = 16 sq in
A = s2
A = 42
A = 16 sq in

15. Example 5: Squares P = 4s P = 4 · 7 P = 28 sq in A = s2 A = 72
Area & Perimeter
Example 5: Squares
Find the perimeter and area of a square whose sides measure 7 inches.
P = 4s
P = 4 · 7
P = 28 sq in
A = s2
A = 72
A = 49 sq in

16. Rectangles: Area & Perimeter A = lw = bh Width = Height Parallel sides
Length = Base
Parallel sides
A = lw = bh

17. Example 6: Rectangles P = 2l + 2w P = 2(9) + 2(4) P = 22 in A = lw
Area & Perimeter
Example 6: Rectangles
Find the perimeter and area of the rectangle.
P = 2l + 2w
P = 2(9) + 2(4)
P = 22 in
A = lw
A = (9)(4)
A = 36 sq in

18. Example 7: Rectangles P = 2l + 2w P = 2(7) + 2(4) P = 22 sq cm A = lw
Area & Perimeter
Example 7: Rectangles
Find the perimeter and area of a rectangle whose length and width measure 7cm and 4cm.
P = 2l + 2w
P = 2(7) + 2(4)
P = 22 sq cm
A = lw
A = (7)(4)
A = 28 sq cm

19. Parallelograms: Area & Perimeter Original figure
Draw a vertical line from top left vertex to the base of the figure
Remove the piece to the left of the vertical line and translate it to the other side of the figure
The new figure is a rectangle or square

20. Parallelograms: Area & Perimeter A = bh height
The shortest distance from the base to the opposite side is the height of the parallelogram
base
The base of a parallelogram can be any one of its sides
A = bh

21. Example 8: Parallelograms
Area & Perimeter
Example 8: Parallelograms
Find the area of the parallelogram.
The base is 6 and
the height is 4.
A = b · h
A = 6 · 4
A = 24 sq un

22. Example 9: Parallelograms
Area & Perimeter
Example 9: Parallelograms
Find the area of the parallelogram.
The base is 9 and the height is 6.
A = b · h
A = 6 · 4
A = 24 sq un 6 9

23. Example 10: Parallelograms
Area & Perimeter
Example 10: Parallelograms
Find the area of each parallelogram. 1
A = b · h
A = (4)(4)
A = 16 sq units 2
A = b · h
A = (4)(3)
A = 12 sq units
A = b · h
A = (7)(3)
A = 21 sq units 3

24. Trapezoids: Area & Perimeter A = ½h(b1 + b2) Parallel sides base 1
height
Parallel sides
base 2
A = ½h(b1 + b2)

25. Example 11: Trapezoids A = ½h(b1 + b2) A = ½(15)(16 + 21)
Area & Perimeter
Example 11: Trapezoids
Find the area of the trapezoid.
A = ½h(b1 + b2)
A = ½(15)( )
A = (7.5)(37)
A = sq cm

26. Example 12: Trapezoids A = ½h(b1 + b2) A = ½(26.6)(19.2+30.4)
Area & Perimeter
Example 12: Trapezoids
Find the area of the trapezoid.
A = ½h(b1 + b2)
A = ½(26.6)( )
A = (13.3)(49.6)
A = sq m

27. A = ½h(b1 + b2) A = ½(21)(8.1+28.2) A = (10.5)(36.3) A = 381.15 sq m
Area & Perimeter
Example 13: Trapezoids
Find the area of the trapezoid.
A = ½h(b1 + b2)
A = ½(21)( )
A = (10.5)(36.3)
A = sq m

28. Independent Practice: Triangles
Area & Perimeter
Independent Practice: Triangles
Find the area of each triangle.

29. Independent Practice: Triangles
Area & Perimeter
Independent Practice: Triangles
Answers.
1. A = 18 sq in A = sq m
3. A = 185 sq m A = sq cm

30. Independent Practice: Parallelograms
Area & Perimeter
Independent Practice: Parallelograms
Answers.
4.2 4 12
5.7 9
9.7
2.3
3.1

31. Independent Practice: Parallelograms
Area & Perimeter
Independent Practice: Parallelograms
Find the area of each parallelogram.
4.2 4 12
5.7
A = 48 sq un
A = sq un 9
9.7
A = 20.7 sq un
A = sq un
2.3
3.1

32. Independent Practice: Trapezoids
Area & Perimeter
Independent Practice: Trapezoids
Find the area of each trapezoid.
3. b1 = 8½ m, b2 = 3¼ m, h = 7¾ m
4. b1 = 16cm, b2 = 9cm, h = 12cm

33. Independent Practice: Trapezoids
Area & Perimeter
Independent Practice: Trapezoids
Answers.
1. A = /189 sq in A = sq ft
3. A = sq m
4. A = 150 sq cm

34. Summary: A = lw = bh A = lw = bh A = ½bh A = bh Area & Perimeter
Formula Review:
A = lw = bh
A = lw = bh
A = ½bh
A = ½h(b1 + b2)
A = bh

35. Area & Perimeter
HOMEWORK

36. Area & Circumference of Circles

37. Objectives: Essential Question: Area & Perimeter
Develop fluency in the use of formulas to solve problems.
Essential Question:
How can I use formulas to find the perimeter and area of simple geometric figures?

38. Circles: Area & Perimeter What do they look like…
A circle is a geometric shape with all points the same distance from the center.
- The circle above is called circle A since the center is at point A. (circles are always named by their centers)

39. Area & Perimeter
HOMEWORK