area/perimeter of combined or partial shapes the trick to calculating the area or perimeter of a...
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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.
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Area/Perimeter Of Combined or Partial Shapes
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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.
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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
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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
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• Can you find the area and perimeter of this figure?
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• 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.
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• The area of a rectangle formula is: A = LW
A = 5x10A = 50
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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
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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
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How would you calculate the perimeter of this shape?
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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.
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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.
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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
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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.