To determine the area of the figure given we need to divide the composite figure into figures in which we know how to find the area. We divide the figure into a triangle, a rectangle and a circle.
The area of a triangle is given by:
where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
The area of the rectangle is given by:
where l is the length and w is the width. For this triangle the length is 9 and the width is 6 then we have:
The area of a circle is given by:
where r is the radius of the circle. The circle shown has a diameter of 6; we know that the radius is half the diameter, then the radius is 3. Plugging the radius, we have:
Now we add the areas of each figure, therefore we have:
