 # Area/Perimeter Of Combined or Partial Shapes

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Area/Perimeter Of Combined or Partial Shapes
The trick to calculating the area or perimeter of a combined or partial shape is to divide up the figure into shapes for which you can find the area and perimeter.

Area/Perimeter Of Combined or Partial Shapes

Using the dotted lines to
divide the shape into 3 rectangles allows you to use the dimensions you are given and the formula for the area of a rectangle to find the areas of the 3 sections. Add those 3 areas together to find the area of the entire figure. For perimeter, add up all the outside side lengths of the figure.

The large rectangle: A = (4 + 10 + 4) 12
= 18  12 = 216 sq. units The small rectangles (same size): A = 10  4 = 40 sq. units (each) Area of total figure: A = = 296 sq. units

Perimeter: Start at the top and add all the side lengths. P = = 76 units

Can you find the area and perimeter of this figure?

Can you find the area and perimeter of this figure? For the area, we have a rectangle attached to half of a circle. We’ll need to find the area of each and then add them together.

The area of a rectangle formula is: A = LW A = 5x10 A = 50

The area of a circle formula
is: A = πr2 The circle’s diameter is 10, so the radius is 5. A = 3.14 x 52 A = 3.14 x 25 A = 78.5

We only have half of a circle,
so the area of the semi-circle is one half of 78.5. Area of semicircle 39.25 Area of rectangle 50 Total area of shape = 89.25

How would you calculate the
perimeter of this shape?

How would you calculate the
perimeter of this shape? Again, we have the rectangular part, which is straight forward, but we also need to figure out the semi-circle part.

Circumference is perimeter for circles
Circumference is perimeter for circles. We’ll use that formula to find the circumference if this was a whole circle. Half of that will be the distance around the semi-circle.

Circumference of the whole circle:
C = πD C= 3.14 x 10 = 31.4 units Circumference of the semi-circle: 31.4 ÷ 2 = 15.7 units Perimeter of the total figure: P = = 35.7

Area/Perimeter Of Combined or Partial Shapes
Try the problems on the bottom of page 161 through page 162 in the book. Check your answers online. Do the GED Practice problems on pages 27 and 28 in the packet, and enter your answers online.