Area of Complex Shapes
This worksheet focuses on calculating the area of complex shapes by decomposing them into simpler geometric figures, suitable for Grade 11 math students.
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Area of Complex Shapes
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Read each question carefully and calculate the area of the complex shapes. Show all your work.
1. Calculate the area of the composite figure below, which consists of a rectangle and a semicircle. Use π ≈ 3.14.
2. A complex shape is formed by a square with side length 6 cm and an equilateral triangle attached to one of its sides. The area of the square is cm², and the height of the equilateral triangle is approximately cm.
3. Find the area of the shaded region if the larger rectangle has dimensions 12 units by 8 units, and the smaller unshaded rectangle inside it has dimensions 6 units by 4 units.
4. A composite shape is made of a square with side length 's' and four semicircles attached to each side. Which expression represents the total area of the shape?
s² + 2π(s/2)²
s² + πs²
s² + 4π(s/2)²
s² + π(s/2)²
5. The area of a complex shape can always be found by adding the areas of the simpler shapes it is composed of.
True
False