Grade 12 Math: Area of Complex Shapes

Area of Complex Shapes

Read each question carefully and calculate the area of the complex shapes shown. Show all your work for full credit. Use π ≈ 3.14 where necessary.

1. Calculate the area of the 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 complex shape is formed by a square with side length 8 meters and an equilateral triangle attached to one of its sides. The area of the square is   square meters, and the height of the equilateral triangle is approximately 6.93 meters. The area of the triangle is approximately   square meters. Therefore, the total area of the complex shape is approximately   square meters.

3. A shape is composed of two identical rectangles, each measuring 5 units by 3 units, and a square with side length 2 units placed between them. What is the total area of this composite shape?

4. A garden plot is shaped like a large rectangle with dimensions 15 meters by 10 meters, but it has a triangular flower bed removed from one corner. The triangular flower bed has a base of 3 meters and a height of 4 meters. What is the area of the remaining garden plot?

5. The area of a complex shape can always be found by summing the areas of simpler shapes it is composed of, or by subtracting the areas of removed shapes.