Finding the Area of Irregular Figures
Learning Outcomes
- Combine area of regular shapes to find the area of irregular shapes.
So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.
example
Find the area of the shaded region.



try it
[ohm_question]146946[/ohm_question]example
Find the area of the shaded region.
Answer:
Solution
We can break this irregular figure into a triangle and rectangle. The area of the figure will be the sum of the areas of triangle and rectangle.
The rectangle has a length of units and a width of units.
We need to find the base and height of the triangle.
Since both sides of the rectangle are , the vertical side of the triangle is , which is .
The length of the rectangle is , so the base of the triangle will be , which is .
Now we can add the areas to find the area of the irregular figure.
The area of the figure is square units.
try it
[ohm_question]146949[/ohm_question]example
A high school track is shaped like a rectangle with a semi-circle (half a circle) on each end. The rectangle has length meters and width meters. Find the area enclosed by the track. Round your answer to the nearest hundredth.
Answer:
Solution
We will break the figure into a rectangle and two semi-circles. The area of the figure will be the sum of the areas of the rectangle and the semicircles.
The rectangle has a length of m and a width of m. The semi-circles have a diameter of m, so each has a radius of m.