Finding area of irregularly shaped surfaces involves finding area of plane surface whose area cannot be calculated from known formula.
Irregular shapes are shapes that cannot be precisely described in terms of geometrical shapes. Their edges and vertices are not uniform.
To estimate of the area of an irregular shape, one can divide the shape into squares each of unit area . By counting the number of small squares, of the irregular shape, we can then estimate the area . consider the diagram below.
Area of irregularly shaped surfaces can be estimated when , we trace the figure on a grid that has squares whose area is 1 cm2 each. We count the squares that are whole covered by the figure and record them. We then count the number of squares that are partially covered by the object and then divided them by two. Add the number of the full square to the half number of the partially covered square to estimate the area covered by the irregularly shaped surface.
study carefully the figure below:
Count the number of squares that are completely covered by the shape, you find that they are 39.
The number of squares that have been touched by the figure (partially covered) are counted as 30.
The area is thus calculated as follow:
Area covered by complete squares = 39 cm2 .
Area covered by partially covered squares = 30/2= 15cm2 .
Therefore the area covered by the figure =( 39 + 15 ) cm2=54 cm2
Hence the estimated area of the given figure is 54 cm2
problem involving Area of irregularly shaped surfaces
Determine the area of the figure below.
procedure:
- count the number of squares that are completely inside the figure.
- count the number of squares that are are bot completely inside the figure but at least touches it.
Problem to exercise
- Trace the palm of your hand on a graph paper then use the method of determining area of irregularly shaped surface to determine the area of your palm.
2. Trace your foot on a grid and estimate it’s area
3. Calculate the area of a garden plot that has a shape like a trapezoid, with one side 12 meters, another side 8 meters, and a height of 5 meters.
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