1. Objective
Apply formulas for perimeter, area, and circumference to composite figures.

2. Remember that the base and height of a triangle are always
perpendicular to each other.
Below are three examples showing the base and height.

3. Find the exact perimeter and shaded area of the composite figure.

4. First we need to find a few more dimensions

5. What would this dimension be?
22 cm

6. How about this dimension?
22 cm
12 cm ?

7. Let’s see what we have so far:
Perimeter = + + + 22
22 cm 12
12 cm 12 22

8. What are we missing? + + + Perimeter = 12 22 12 22 22 cm 3 3 cm 3 3 cm

9. So let’s add those dimension!+ + + + + + +
Perimeter = 12 22 12 22
22 cm 3
3 cm
3 cm 3
12 cm
12 cm
3 cm 3 3
3 cm
22 cm

10. Something is wrong, find the error.+ + + + + + +
Perimeter = 12 22 12 22 3 3 3 3
The 3 cm’s are for the radius not the curve
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

11. How do we find the length along a curve?+ + + + + + +
Perimeter = 12 22 12 22
Before we answer that lets get rid of the extra information
for a minute and look at just the four curves.
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

12. How do we find the length along a curve?+ + + + + + +
Perimeter = 12 22 12 22
Now let’s move the curves around.
What shape do all four curves together make?
What is the formula for finding the distance around a circle?
3 cm
3 cm
And r = ? or
3 cm
3 m

13. Simplify the perimeter+ + + +
Perimeter = 12 22 12 22
Perimeter = 58 +
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

14. Now let’s find the area!
Get rid of all the excess information for a minute
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

15. This figure is made of many shapes.
Can you name them?
This is easier if we take the edges and extend them until they meet.
Rectangle
Large circle
4 quarter circles
1 small circle
or when put together?

16. So, the area is? __ __ Something is wrong, find the error! Area = + +
__ __
Area =
Area =
Rectangle
Large circle
1 small circle

17. Now apply the formula’s
__ __
Area =
Rectangle
Large circle
1 small circle
Area of rectangle = (l)(w)
__ __
Area =
(l)(w)

18. Now put in the numbers __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(l)(w)
Let’s bring our dimension back
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

19. Now put in the numbers __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(w)
(l)(w)
What does (l) =?
Does (l) =28?
Does (l) = 22 ?
(l)
22 cm
3 cm
3 cm
12 cm
12 cm
3 cm
3 cm
22 cm

20. Now put in the numbers __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(w)
(28)(18)
What does (w) =?
(l)
22 cm
3 cm
3 cm
(w)
12 cm
12 cm
3 cm
3 cm
22 cm

21. Now the large circle __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(18)
Is the radius of the large circle half of 22 cm?
What is the radius of the large circle=?
(28)
22 cm
3 cm
3 cm r
(18)
12 cm
12 cm
3 cm
3 cm
22 cm

22. Now the large circle __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(18)
What do you think when the radius is shown like this?
So now what is the radius of the large circle?
(28)
22 cm
3 cm
3 cm r
(18)
12 cm
12 cm
3 cm
3 cm
22 cm

23. And last is the small circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(18)
This one should be easy, what is the radius of the small circle?
(28)
22 cm
3 cm
3 cm 9
(18)
12 cm
12 cm
3 cm
3 cm
22 cm

24. Area = 221.3 cm 2 Last step __ __ __ __ Area = Rectangle Large circle
__ __
Area =
Rectangle
Large circle
1 small circle
__ __
Area =
(28)(18)
Put this into the calculator and give your answer to the nearest tenth
(remember to units, cm) 2
Area = cm