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 formulafor 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 = 216 + 40 + 40

= 296 sq. units

Perimeter:Start at the top and add all the side lengths. P = 10 + 4 + 4 + 12 + 4 + 4 + 10 + 4 + 4 +12 + 4 + 4 = 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 = 5x10A = 50

The area of a circle formulais: A = πr2

The circle’s diameter is 10, so the radius is 5.A = 3.14 x 52

A = 3.14 x 25A = 78.5

We only have half of a circle, so the area of the semi-circleis one half of 78.5.Area of semicircle 39.25Area of rectangle 50

Total area of shape 50 + 39.25 = 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. 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 = πDC= 3.14 x 10 = 31.4 units Circumference of the semi-circle: 31.4 ÷ 2 = 15.7 units Perimeter of the total figure:P = 20 + 15.7 = 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.