Area of Irregular Shapes

Area of Irregular Shapes Worksheet

Read each question carefully and calculate the area of the irregular shapes. Show all your work and include appropriate units in your final answers. You may decompose the shapes into simpler geometric figures such as rectangles, triangles, and semicircles.

1. Calculate the area of the irregular shape shown below. All angles are right angles. Dimensions are in meters.

2. A swimming pool is shaped like a rectangle with a semicircle attached to one of its longer sides. The rectangular part is 12 meters long and 6 meters wide. Calculate the total area of the pool. Use π ≈ 3.14. Round your answer to two decimal places. The area of the rectangular part is   m², and the area of the semicircular part is   m². The total area of the pool is   m².

3. Find the area of the shaded region in the figure below. The outer rectangle has a length of 15 cm and a width of 10 cm. The unshaded inner rectangle has a length of 10 cm and a width of 6 cm.

4. A garden is in the shape of a trapezoid and a triangle, as shown. What is the total area of the garden?

5. A plot of land is in the shape of a rectangle with a triangular section removed from one corner. The rectangle measures 20 meters by 15 meters. The removed triangular section has a base of 8 meters and a height of 5 meters. What is the remaining area of the plot of land?