Area Problem Solving
Sometimes you can use the simple area formulas forrectangles,三角形s, andcirclesin combination to find the areas of more complicated shapes.
Example 1:
What is the area of the shaded region?
The area of the shaded region is the difference between the areas of the rectangle and the square.
The dimensions of the rectangle arebyand so the area istimes, that issquare units.
Each side of the square measuresunits and so the area istimes, that issquare units.
Therefore, the area of the shaded region issquare units.Example 2:
Find the total area of the shaded region. (In the figure, all angles are right angles.)
The given figure can be divided intosquares and a rectangle as shown.
The total area is the sum of the areas of the rectangle and the squares.
The dimensions of the rectangle arebyand so the area istimes, that issquare units.
All the three squares have each sideunits long and so the area of each of them istimes, that issquare units.
Therefore, the total area issquare units.
Example 3:
Ifis a right triangle andis a semicircle, find the total area of the figure.
The total area is the sum of the areas of the triangle and the semicircle.
We have the length of a side and that of the altitude to the side of the triangle. So, the area of the triangle is
Sinceis a semicircle,is a diameter. Butis also thehypotenuseof the right triangle.
Use thePythagorean Theoremto find the length.
So, the diameter of the semicircle isunits and so the radius isunits.
The area of a semicircle of radiusunits is.
Therefore, the total area is about.