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

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

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

First we need to find a few more dimensions

What would this dimension be? 22 cm

How about this dimension? 22 cm 12 cm ?

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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 = 221.3 cm