How to Calculate the Area of Shaded Regions

Finding the area of a shaded region can seem challenging at first, especially to students who are just learning the concept of area. By breaking each shaded region down into its basic parts and using some simple area formulas, this task becomes much easier. The key is to take the time to analyze the shape and break it down into regular shapes, known as polygons, that have area formulas. A little bit of practice will make this challenging task become easy for most math students!

Difficulty: Moderately Easy

Instructions

Things You'll Need:

• Paper
• Pencil

How to Calculate the Area of Shaded Regions

1. Decide whether or not the shaded region is a square, rectangle, or triangle. If it is a square, use the formula side * side = area. If it is a triangle, use the formula 1/2 base * height = area. If it is a rectangle, use the formula length * width = area.

2. Break up any shapes that are not one of the three basic polygons by drawing lines in it so that it becomes a combination of rectangles, squares, and triangles. This will usually give you a shape made up of several different sized rectangles.

3. Calculate the area of the rectangles or other shapes you have just made with your lines. You may have to do some calculations to find unknown sides. Use the sides you do know to figure out the lengths of any unkown sides.

4. Add together all of the areas you have calculated. This should be the area of the entire shaded region.

5. Subtract the area of any portions of the shape that are not shaded. For instance, if there is a square section in the middle of the shape that is unshaded, figure out the area of the entire shape, then the area of the square in the middle, and subtract the area of the square from the total.

6. Check your answer to make sure it seems reasonable. Then, label it with square units.

Tips & Warnings

• Always label your answer with square units, such as square inches or meters squared. Your teacher will be looking for this as part of your answer.
• Never calculate the area of the same part of the shape twice. This will cause your answer to be incorrect. Use caution when drawing the lines on the shape so that they do not create overlapping shaded areas.

Resources

• Common Area Formulas