Finding Area of Compound Figures

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

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.

Finding Area of Compound Figures – Example 1

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.
\(56+8=64 in^2\)