Composite Figure

Question

Determine the total perimeter AND area of the following crayon (composite figure) to (to one decimal place):

the tip=14cm

the body=35cm

the bottom with a radius of = 5cm

Answer 1

Hi Greg

 

You have to start calculating the diameter of the half circle:  D = 10 cm  (if radius= 5 cm)  The perimeter is pi*r 

 

 

Now you have a rectangle with large (L) = 35 cm  and width (W) = 10 cm (the same diameter than the half-circle)

The area is L*W   The perimeter is 2L + 2W. But you have to consider only 2L as the perimeter of this composed figure.

 

The tip is a triangle with height (h) = 14cm and base (b) 10 cm.  The area is b*h/2   The tricky step is the calculation of the triangle's perimeter: See following figure:

 

 

 

                   *

                /   |\                

              /     |  \              

             /      |    \            

         a /       |      \ c        

           /        |        \        

          /         |h=14  \       

         /          |            \    

        /           |              \  

       /            |                \

       ==============

                    b (=10 cm)

 

The triangle's perimeter is : a + b +c  

By construction, the triangle has the same side lengths a = c  and the height line divide the base in two equal sides, 5 cm length each one.

 

For estimating c (or, a) you have to use the Pythagoras's principle:   h² + (b/2)² = c²  

 

                                                                                                   c = sqrt( (14)² + (5)²) = 14.9 cm = a

 

The tip of this composed figure is then: a + c = 29.8 cm

 

Solution:

The composed shape's perimeter is :

pi*r + 2L + 29.8  =  pi*5 + 2(35) + 29.8

 

The composed shape's area is :

0.5*pi*r² + L*W + b*h/2  = 0.5*pi*(5)² +(35)*(10) + (14)*(10)/2

 

Answer 2

A_triangle = (0.5)(14)(10)

A_rectangle = (35)(10)

A_semicircle = (0.5)(5²)(π)

 

Calculate each and add to determine area of composite.