Finding Area of Compound Figures

A step-by-step guide to finding the area of compound figures

Here are the general steps to find the area of a compound figure:

1. Identify the individual shapes: Look at the compound figure and identify the different shapes that make it up. These shapes may include squares, rectangles, triangles, circles, or other shapes.
2. Break the figure down: Divide the compound figure into these individual shapes by drawing lines or visualizing how they fit together.
3. Find the area of each shape: Use the appropriate formula for each shape to find its area. For example, the area of a rectangle is length x width, while the area of a circle is pi x radius squared.
4. Add the areas together: Once you have found the area of each shape, add them all together to get the total area of the compound figure.
5. Check your work: Double-check your calculations to make sure you have correctly found the area of each shape and added them together accurately.

Keep in mind that when finding the area of compound figures, you may need to subtract areas of shapes that overlap or subtract areas of shapes that are cut out of larger shapes.

Additionally, it may be helpful to label the different shapes and dimensions to keep track of your calculations.

Finding Area of Compound Figures – Example 1

Calculate the area of this shape.

Solution:
Step 1: Divide this shape into 2 rectangles.

Step 2: Find the area of each shape.
\(12×10=120\)
\(5×3=15\)
Step 3: Add them together.
\(120+15=135 yd^2\)

Finding Area of Compound Figures – Example 2

Calculate the area of this shape.

Solution:

Step 1: Divide this shape into regular shapes.

Step 2: Find the area of each shape.
\(7×8=56\)
\(4×4=16, \frac{1}{2}×16=8\)
Step 3: Add them together.
\(56+8=64 in^2\)