Finding Areas of Polygons and Trapezoids

Mrs. Nelson introduces the lesson on polygons, focusing on calculating the area by decomposing and rearranging shapes. The lesson covers parallelograms and triangles, explaining how to find their areas. The main focus is on applying these strategies to trapezoids, using methods like enclosing, subtracting, and rearranging to form rectangles. The lesson concludes with a summary of the strategies used to find the area of various polygons.

What is the main objective of the lesson on polygons?

• To draw different types of polygons

• To memorize the formulas for all polygons

• To reason about the area of any polygon by decomposing and rearranging it

• To learn the history of polygons

How can the area of a parallelogram be found?

• By decomposing and rearranging it into a rectangle

• By measuring its perimeter

• By dividing it into circles

• By counting the number of sides

What is the relationship between the area of a triangle and a parallelogram with the same base and height?

• The area of the triangle is half the area of the parallelogram

• The area of the triangle is one-third the area of the parallelogram

• The area of the triangle is the same as the parallelogram

• The area of the triangle is double the area of the parallelogram

Which of the following is NOT a strategy to find the area of a trapezoid?

• Rearranging into a circle

• Enclosing and subtracting

• Rearranging into a rectangle

• Decomposing into triangles and a rectangle

What is one method to find the area of a trapezoid?

• By drawing a diagonal

• By counting the number of vertices

• By measuring its perimeter

• By enclosing it in a rectangle and subtracting the extra parts

How can a trapezoid be rearranged to find its area?

• By rotating it into a circle

• By stretching it into a parallelogram

• By decomposing it into two triangles and a rectangle

• By folding it into a cube

What is the area of the rectangle formed by rearranging the trapezoid in the example?

• 18 square units

• 15 square units

• 12 square units

• 21 square units

What is the formula used to find the area of the rectangle in the example?

• Base minus height

• Base divided by height

• Base times height

• Base plus height

What is emphasized as a key strategy for finding the area of polygons?

• Drawing accurate diagrams

• Decomposing and rearranging

• Memorizing all formulas

• Using a calculator

What is the final example used to illustrate the lesson's objective?

• A circle

• A trapezoid

• A square

• A hexagon