Exercises


Questions 1 and 2 refer to the following figure.

A compound shape made up of two connected rectangles, the first with length 12 cm and width 7 cm, the second with length 18 cm and width 5 cm.

  1. Calculate the perimeter of the figure in two different ways: one that involves determining the lengths of all the segments in the diagram, and one that does not.
  2. Calculate the area of the figure in two different ways: one that involves addition and one that involves subtraction.

Questions 3 to 5 refer to the following information.

Michael is building a swimming pool in the shape of a rectangle with a semi-circle attached to the shorter side. The dimensions of the rectangular part of the pool is \(4.3\) m by \(8.5\) m. The pool will be surrounded on all sides by a cement deck \(1\) m wide.

  1. Michael wants to buy a pool cover that will just cover his pool.
    If the pool cover material costs \($11.50\)/m2, what will be the total cost of the cover?
  2. What is the area of the cement needed to create the deck?
  3. Michael needs to build a fence around the entire pool and deck area. He already has a \(1.5\) m wide gate but needs to buy the rest of the fencing. What length of fencing does he need?
  4. The shape below has an area of \(100\) cm2. What is the perimeter of the shape?

    A circle that is a missing a 60 degree arc.

  5. In Figure 1, a circle with radius \(10\) is inscribed in a square. In Figure 2, a square is inscribed in a circle of radius \(10\). In each figure, the area between the two shapes is shaded. Which figure has the greater shaded area?

    Figure 1

    Figure 2

  6. Hunter has two shapes, Shape 1 and Shape 2. He can makes a Composite shape by adding Shape 2 to Shape 1 or by subtracting Shape 2 from Shape 1.
    1. What could Shape 1 and Shape 2 be so that the perimeter of the Composite shape is less than the perimeter of Shape 1?
    2. What could Shape 1 and Shape 2 be so that the perimeter of the Composite shape is equal to the perimeter of Shape 1?
    3. What could Shape 1 and Shape 2 be so that the perimeter of the Composite shape is greater than the perimeter of Shape 1?

Questions 9 and 10 refer to the following information.

A composite shape is formed by two overlapping congruent circles with radius \(8\) cm and centres \(A\) and \(C\). The circles intersect at points \(B\) and \(D\) so that \(ABCD\) is a square.

  1. Determine the perimeter of the composite figure.
  2. Calculate the area of the composite figure.