Area of irregular shapes
To find the area of irregular shapes, the first thing to do is to divide the irregular shape into regular shapes that you can recognize such as
triangles, rectangles, circles, squares and so forth...
Then, find the area of these individual shapes and add them up!
Example #1:
The figure above has two regular shapes. It has a square and half a circle
Find the area for each of those two shapes and add the results
Square
Area
_{square} = s
^{2}
Area
_{square} = 4
^{2}
Area
_{square} = 16
Circle
Area
_{circle} = pi × r
^{2}
Notice that the radius of the circle is 4/2 = 2
Area
_{circle} = 3.14 × 2
^{2}
Area
_{circle} = 3.14 × 4
Area
_{circle} = 12.56
Since you only have half a circle, you have to multiply the result by 1/2
1/2 × 12.56 = 6.28
Area of this shape = 16 + 6.28 = 22.28
Example #2:
The figure above has three regular shapes. Starting from top to bottom, it has a triangle, a rectangle,
and a trapezoid
Find the area for each of those three shapes and add the results
Triangle
Area
_{triangle} = (base × height)/2
Area
_{triangle} = (3 × 4)/2
Area
_{triangle} = 12/2
Area
_{triangle} = 6
Rectangle
Area
_{rectangle} = length × width
Area
_{rectangle} = 3 × 10
Area
_{rectangle} = 30
Trapezoid
Area
_{trapezoid} = ((b
_{1} + b
_{2}) × h)/2
Area
_{trapezoid} = ((3 + 5) × 2)/2
Area
_{trapezoid} = (8) × 2/2
Area
_{trapezoid} = 16/2
Area
_{trapezoid} = 8
Area of this shape = 6 + 30 + 8 = 44
Example #3:
The area of irregular shapes can be as challenging as this last example, so study it carefully!
The figure above has 4 regular shapes. It has a triangle, two rectangles,
and half a circle
Find the area for each of those 4 shapes and add the results
Rectangle
Area
_{rectangle} = length × width
Area
_{rectangle} = (12 × 16)
Area
_{rectangle} = 192
Since we have two of the same rectangle, the area is 192 + 192 = 384
Triangle
Notice that the longest side of the rectangle is the base of the triangle and the short side of the rectangle is the height of the triangle
So,
Area
_{triangle} = (base × height)/2
Area
_{triangle} = (16 × 12)/2
Area
_{triangle} = (192)/2
Area
_{triangle} = 96
Circle
To get the area of the half circle, we need to know the diameter
Notice that the diameter is the hypotenuse of a right triangle, so use the Pythagorean Theorem to find the length of the diameter
c
^{2} = a
^{2} + b
^{2}
c
^{2} = 12
^{2} + 16
^{2}
c
^{2} = 144 + 256
c
^{2} = 400
c = √400
c = 20
Therefore, the diameter is 20. Since the diameter is 20, the radius is 10
Area
_{circle} = pi × r
^{2}
Area
_{circle} = 3.14 × 10
^{2}
Area
_{circle} = 3.14 × 100
Area
_{circle} = 314
Since you only have half a circle, you have to multiply the result by 1/2
1/2 × 314 = 157
Area of this shape = 384 + 96 + 157 = 637
Here we go! I hope these good examples were very helpful in helping you how to get the area of irregular shapes.
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