Area of irregular shapesTo 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... Example #1: 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: 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! 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. Any questions on how to get the area of irregular shapes? Contact me. 




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