Grade 12 Math: Area of Composite Shapes

Area of Composite Shapes

Read each question carefully and calculate the area of the composite shapes. Show all your work and include appropriate units.

1. Find the area of the composite shape below, which consists of a rectangle and a semicircle. The rectangle has a length of 10 cm and a width of 6 cm. The semicircle is attached to one of the 6 cm sides.

2. A composite figure is made up of a square with side length 8 meters and an equilateral triangle attached to one of its sides. The area of the square is   m², and the height of the equilateral triangle is approximately 6.93 meters. The area of the equilateral triangle is   m². Therefore, the total area of the composite figure is   m².

3. A rectangular garden measures 15 feet by 20 feet. A circular pond with a radius of 5 feet is located in the center of the garden. What is the area of the garden NOT covered by the pond? (Use π ≈ 3.14)

4. A company logo is designed using a large square with side length 12 inches, with a smaller square cut out from its center. The smaller square has a side length of 4 inches. Calculate the area of the logo.

5. To find the area of a composite shape, you always subtract the areas of its simpler components.

6. Consider a shape composed of a right-angled triangle and a rectangle. The triangle has legs of 8 cm and 6 cm. The rectangle shares the 6 cm side with the triangle and has a length of 10 cm. Find the total area of this composite shape.

7. Match the composite shape description with the correct method for calculating its area.