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 = s²

Area _square = 4²

Area _square = 16

Circle

Area _circle = pi × r²

Notice that the radius of the circle is 4/2 = 2

Area _circle = 3.14 × 2²

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 = ((b₁ + b₂) × 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

c² = a² + b²

c² = 12² + 16²

c² = 144 + 256

c² = 400

c = √400

c = 20

Therefore, the diameter is 20. Since the diameter is 20, the radius is 10

Area _circle = pi × r²

Area _circle = 3.14 × 10²

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.