Area of Irregular Figures Worksheet
Calculate the area of complex irregular figures by decomposing them into simpler geometric shapes. Includes various problem types for Grade 12 Math.
Includes
Standards
Area of Irregular Figures
Name:
Date:
Score:
Read each problem carefully and calculate the area of the irregular figures. Show all your work. Remember to decompose complex figures into simpler, recognizable shapes.
1. Calculate the area of the figure shown below. All angles are right angles. Dimensions are in meters.
Show your work:
2. A swimming pool is shaped like a rectangle with a semi-circle attached to one of its longer sides. The rectangular part is 10 m by 6 m. The diameter of the semi-circle is equal to the width of the rectangle. The area of the pool is approximately square meters. (Use π ≈ 3.14)
3. Consider an irregular figure formed by a square with side length 5 cm and an equilateral triangle attached to one of its sides. What is the total area of this figure?
25 + (25√3)/4 cm²
25 + (5√3)/2 cm²
50 + (25√3)/4 cm²
50 cm²
4. A garden plot is in the shape of a trapezoid with parallel sides of length 12 ft and 18 ft, and a height of 10 ft. A rectangular flower bed of 4 ft by 6 ft is located within the garden. What is the area of the garden remaining for vegetables?
5. The area of an irregular polygon drawn on a coordinate plane can be found using the Shoelace Formula if the coordinates of its vertices are known.
True
False