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:
[tex]A=\frac{1}{2}bh[/tex]
where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
[tex]A=\frac{1}{2}(6)(6)=\frac{36}{2}=18[/tex]
The area of the rectangle is given by:
[tex]A=lw[/tex]
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:
[tex]A=(9)(6)=54[/tex]
The area of a circle is given by:
[tex]A=\pi r^2[/tex]
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:
[tex]A=(3.14)(3)^2=28.26[/tex]
Now we add the areas of each figure, therefore we have:
[tex]18+54+28.26=100.26[/tex]
