Areas of Complicated Shapes?

Question

Hi. I need a solution to this problem. The question is find the perimeter and area of the shape. In my book it says that the answer is : Perimeter is 49.7cm and the Area is 129.3cm2.
The measurements are 4cm, 5cm, 6cm and 7 cm.

A rough image of the shapes are here:
http://img373.imageshack.us/my.php?image=areapm1.png

I know how to do areas of complicated shapes. You basically use the areas of shapes individually etc and then add them up, but this one is giving me problems.

When i try and do it i work with the top rectangle 6x7= 42cm2. Bottom rectangle 4 x 12 = 48cm2. And for the semicircle i use the area of circle foruma 'Pi * r2" and then divide 2. The radius seems to be 5cm when i do it. So 3.14*5 subtact 2 = 39.25cm2. I get the total area 129.25cm2 instead of the correct answer which is 129.3cm2. I was wondering if some people could post a guide on how to work it out and tell me what i am doing wrong. Also can you explain the perimeter. Thank you very much.

Answer 1

I get 129.2699081:

42 (6x7, upper rectangle) +
48 (4x(7+5), lower rectangle) +
39.2699081 (pi*r*r/2 for semicircle area)
------------------------
129.2699081

I'd round that off to 129.27 or 129.3. Maybe if you used more than two digits for pi (try 3.1416 instead of just 3.14).

==============
Perimeter:

7 (top edge) +
6 (first drop on left) +
5 (extension further left) +
4 (second drop to the bottom) +
12 (5+7, bottom edge) +
15.708 (pi*r*2/2 = semicircle arc)
--------------------------
49.708 cm

I'd round that off to 49.7cm.

Answer 2

The area is 12*4+7*6 +.5pi*5^2 =48+42+39.23=129.2699.
Since all your numbers (4,5,6,7) are accurat to onne significant digit, you should round your answer to 129.3.

The perimeter is 12+4+5+6+7+5*pi
= 34 + 5 pi = 33 + 15.7= 49.7

Answer 3

Um, your answer is the same as the book's, but the book's answer is rounded up to the nearest tenth.

Perimeter is just the perimeter of the solid sides + 2pi*r/2 for the semi-circle.

Answer 4

Are you sure your book isn't just rounding up?