1. Formulas for Geometry: Perimeter & Area

2. Mathematicians have created formulas to help you find the perimeter and areas of different shapes. Use the formulas to solve your problems!

3. Perimeter
Any shape’s “perimeter” is the distance on the outside of the shape…like a fence around a yard.

4. Perimeter
To calculate the perimeter of any shape, just add up each line segment of the “fence” around the shape.

5. Perimeter Triangles have 3 sides…add up each sides length. 8 8
8+8+8=24
The Perimeter is 24 8

6. Practice: Find the perimeter1) 5 3 4
So add up = 12 units
Free powerpoint template:

7. Perimeter
A square has 4 sides of a fence 12 12 12
=48 12

8. Perimeter
Sometimes, problems may only give you two measurements for a square or rectangle.
No problem. Remember that all the sides of a square is the same measure and the opposite sides of a rectangle are the same measure.

9. Remember
Squares ALL sides are equal…so if they give you one side, you know ALL the sides
Length=the Largest side
If they “leave” numbers out, they are equal to their opposite side.

10. The Same!!
If the bottom is 15…the top is… 15

11. Square/Rectangle Formula
Perimeter=2L + 2W or 2(L + W)
P= 2(5) + 2(4) P=2(5 + 4)
P= P= 2(9)
P= P=18
Or just ADD the 4 sides!! 4 10 5
Free powerpoint template:

12. Other shapes Just add up EACH segment 10 10 10
8 sides, each side 10 so =80

13. Circumference of a Circle
Perimeter/Circumference = pi x diameter
Pi is always 3.14 or 3 (for estimation)
Circumference is a fancy name for perimeter
The diameter is a line from one side to the other side of a circle through its origin (It’s twice the radius)
If the radius is 5, then the diameter is 10

14. Practice: Use the formula C = πd
Find the circumference of this circle with a diameter of 10 cm.
D = 10 so multiply (10)(3.14) = 31.4 cm
Free powerpoint template:

15. Finding the Area of a shape

16. Area Area is the ENTIRE INSIDE of a shape
It is always measured in “squares” (square inch, or square feet or whatever unit…)

17. AREA
Square units means that “that” many squares fit inside that shape (if measured in feet…it’s feet…if meters…it’s meters. In this example the area is 4 square units…note 4 squares fit) 1 2 3 4
2 units (ft, in, m)

18. Area of Squares/Rectangles
Length x Width=Area 2
Length(2) xWidth(2) = 4 square units

19. Parallelogram Area
Same idea as squares & rectangles, but they change the words to Base (length: bottom of shape) and height (similar to width but MUST be 90 degrees to the base.)

20. Parallelogram Area Area=Base x Height The diagonal line is NOT
the height!!! 5
Height (width) 8
BASE (length)
Base 8 x Height 5 = Area 40

21. Formula for area of squares
Area= S^2
Area= Side x Side (side squared) (just a different way of saying length x width)
Side one
Side two

22. Different Names/Same idea
Length x Width = Area
Side x Side = Area
Base x Height = Area (Height must be
90 degrees to the base. NOT the slanted
side’s length.)

23. Area of a Triangle ½ Base x Height = Area
(It’s ½ because ½ of the “square” is missing)
Height 5
Base 8
Height
½ Base x Height = Area
½ (8) x = Area
x = 20
Base

24. Area of a Circle

25. Area of a circle 5
Radius
Area=3.14 x (5 x 5)
Perimeter = 3.14 x 10

26. 
For most tests you will have the formulas given to you. Just remember which one to use for which shape and you’ll do fine.