Finding the Area of Polygons by Decomposing

This lesson teaches how to find the area of various polygons by decomposing them into simpler shapes like triangles, rectangles, parallelograms, and trapezoids. It reviews the formulas for these basic shapes and provides examples of finding the area of a pentagon and an irregular polygon by breaking them into known shapes. The lesson emphasizes the importance of using known shapes to simplify the process and avoid common mistakes.

What is the formula for finding the area of a triangle?

• Base times height divided by 2

• Base plus height

• 1/2 times base times height

• Base times height

How can you find the area of a trapezoid?

• Add the bases, divide by 2, then multiply by the height

• Add the bases and multiply by the height

• Multiply the base by the height and divide by 2

• Multiply the base by the height

When decomposing a pentagon into simpler shapes, which two shapes were used in the example?

• Two trapezoids

• Two triangles

• A rectangle and a triangle

• A triangle and a trapezoid

What is the area of the triangle in the pentagon example?

• 12 square units

• 44.5 square units

• 24 square units

• 32.5 square units

In the irregular polygon example, what shapes were used to find the area?

• Parallelograms

• Triangles

• Rectangles

• Trapezoids

What is the total area of the irregular polygon in the example?

• 80 square units

• 44.5 square units

• 108 square units

• 28 square units

What is the key takeaway from the lesson on finding the area of polygons?

• Always use the same shape to decompose polygons

• Decompose polygons into shapes you know how to calculate the area for

• Only use triangles for decomposition

• Avoid using parallelograms in decomposition