Area of Complex Shapes Worksheet
Calculate the area of various complex shapes by decomposing them into simpler geometric figures. Includes problems involving rectangles, triangles, and circles.
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Area of Complex Shapes
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Read each question carefully and calculate the area of the complex shapes shown. Show all your work.
1. Find the area of the shape below.
2. A composite shape is made of a rectangle with dimensions 8 cm by 6 cm and a triangle with a base of 6 cm and a height of 4 cm attached to one of the 6 cm sides. The total area of the composite shape is square centimeters.
3. Calculate the area of the shaded region in the figure below. Assume the larger rectangle has dimensions 12 units by 8 units, and the unshaded square cut out from its center has sides of 4 units.
4. A semi-circle is placed on top of a rectangle. If the rectangle has a length of 10 meters and a width of 6 meters, what is the total area of the composite shape? (Use π ≈ 3.14)
60 m²
74.13 m²
83.13 m²
90 m²
5. A garden is shaped like a large rectangle with a triangular flower bed removed from one corner. The large rectangle is 15 feet long and 10 feet wide. The triangular flower bed has a base of 5 feet and a height of 4 feet. What is the area of the garden?