Area of Irregular Shapes

Not all shapes are perfect rectangles or circles. Many real-world shapes are irregular, meaning they have unusual outlines. You can still find their area by breaking them into simpler shapes and adding the pieces together.

Breaking Shapes Apart

An L-shaped room can be split into two rectangles. Find the area of each rectangle, then add them together. A T-shape can also be broken into rectangles.

This works for any shape. Look for places to draw lines that create rectangles, triangles, or other shapes you know how to measure. Then add up all the areas.

Estimation Methods

Sometimes a shape is so odd that you cannot break it into neat pieces. In that case, you can estimate the area using a grid. Place the shape on graph paper and count the squares it covers.

Count full squares first. Then look at partial squares. If about half a square is covered, count it as half. Add everything up for a good estimate of the area.

Fun Facts

• Surveyors measure the area of odd-shaped land plots using special math and GPS tools.
• The area of your hand can be estimated by tracing it on graph paper and counting squares.
• Architects find the area of oddly shaped buildings by breaking the floor plan into simple shapes.

Did You Know?

Ancient Egyptians used a method similar to breaking shapes apart to measure farm fields after the Nile River flooded and changed the field boundaries every year!