For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Area of the shaded region square cm

Perimeter of the shaded region cm

Solution:

Radius of the quarter of circle = 12 cm

Area of the shaded region = Area of quarter of circle – Area of the triangle

                                              square cm.

Area of the shaded region square cm

Using Pythagoras theorem,

Taking square root on both sides of the equation, we get

cm

Perimeter of the quadrant of a circle =

                                                              cm

Perimeter of the shaded region = cm

                                                    cm

Hence area of the shaded region square cm

Perimeter of the shaded region cm

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~courtney