Exploring Area of Polygons

Exploring the Area of a Parallelogram Objective: Students will derive the formula for the area of a parallelogram. Materials: Index Cards Ruler Scissors Tape

Step 1: Find the Area of your index card.

Step 2: Use a straightedge to draw a line through one of the vertices of your index card.

Step 3: Cut out the triangle Step 3: Cut out the triangle. Tape the triangle to the opposite side to form a parallelogram.

Think About It How does the area of the parallelogram compare to the area of the rectangular index card?

Think About It 2. How do their bases compare? 3. How do their heights compare?

Think About It Write a conjecture about the formula for the area of a parallelogram.

Exploring the Area of a Triangle Objective: Students will derive the formula for the area of a triangle. Materials: Grid paper Colored pencils or markers Scissors

Step 1: Draw a triangle on grid paper Step 1: Draw a triangle on grid paper. Then draw a rectangle that encloses the triangle. Write down the dimensions of the rectangle.

Step 2: Cut out the rectangle Step 2: Cut out the rectangle. Then cut the triangles out of the rectangle.

Step 3: Arrange the two smaller triangles to cover the area of the large triangle .

Think About It Do the two smaller triangles cover the same area as the large triangle?

Think About It 2. How is the area of the large triangle related to the area of the original rectangle?

Think About It Use the dimensions of the rectangle in step 1 to find the area of the rectangle, then use your answer to find the area of the large triangle.

Use the diagram below to write a conjecture about the area of a triangle given its base b and its height h.

Exploring the Area of a Trapezoid Objective: Students will derive the formula for the area of a trapezoid. Materials: Grid Paper Ruler Scissors Tape

Step 1: On grid paper, cut out two identical trapezoids Step 1: On grid paper, cut out two identical trapezoids. Label the bases b1 and b2, respectively, and label the heights h.

What is the shape formed by the two identical trapezoids? Step 2: Then turn one trapezoid upside down and tape it to the other trapezoid as shown What is the shape formed by the two identical trapezoids?

Think About It Write an expression to represent the base of the parallelogram you created.

Think About It 2. Write an expression to represent the area of the parallelogram you created.

Think About It How does the area of each trapezoid compare to the area of the parallelogram you created?

Think About It Write a conjecture about the formula for the area of the trapezoid.

Exploring the Area of a Circle Objective: Students will derive the formula for the area of a circle. Materials: Paper Compass Ruler Scissors

Step 1: Use a compass to draw a circle on a piece of paper Step 1: Use a compass to draw a circle on a piece of paper. Cut the circle out. Fold the circle in half, four times.

Step 2: Cut the circle along the fold lines to divide the circle into 16 equal wedges.

Step 3: Arrange the wedges to form a shape resembling a parallelogram Step 3: Arrange the wedges to form a shape resembling a parallelogram. The base and height of the parallelogram are labeled.

Think About It 1. How does the area of the original circle compare to the area of the parallelogram you created?

Think About It 2. Write an expression for the height of the parallelogram you created.

Think About It 3. Write an expression for the base of the parallelogram you created.

Think About It 4. Write an expression for the area of the parallelogram you created.

Think About It 5. Use the fact that to rewrite the area.

Think About It 6. Use the fact that to rewrite the area.

Think About It Write a conjecture about the formula for the area of a circle.

NCTM-Circle Lesson Circle Applet