Professional Development
SCMP January 2009
Discovering Area Formulas
1. Draw a rectangle on colored grid paper. Count the squares then see that this
matches the Area Formula: A = l ⋅ w , but then rename the sides as base and
height rather than length and width so that the formula is now A = b ⋅ h . Cut out
the rectangle and glue to plain paper with the formula written next to the figure.
2. Draw and cut out another rectangle. Label the base and height. Discuss the
formula for this shape. A = b ⋅ h Cut the rectangle into 2 pieces that you can
rearrange to make a parallelogram that has no right angles. Glue the
parallelogram to the plain paper. Identify the base and height of the rectangle
on the parallelogram. Use this picture to see the formula for the area of a
parallelogram and write it next to the figure. A = b ⋅ h
3. Cut out 2 identical triangles from colored plain paper. Label the base and height
of each triangle the same. Be sure to draw the height perpendicular to the base.
Rearrange the 2 triangles to form a parallelogram and glue onto the plain white
paper. Discuss how the area of one of the triangles could be found by using the
area of the parallelogram. (i.e. Half of the parallelogram) Write the area
b⋅h
1
formula for the triangle next to the figure.
A=
or A = ⋅ b ⋅ h
2
2
4. Go back to “Shapes” handout and calculate the area of each region using the
formulas. Compare exact answers€to “estimates” and discuss.
5. Recall what a trapezoid looks like. Cut out 2 identical trapezoids. Label the
“top”, “bottom”, and height of each trapezoid the same. Rearrange the 2
trapezoids to form a parallelogram and glue onto the plain white paper. Discuss
how the area of one of the trapezoids could be found by using the area of the
parallelogram. (i.e. Half of the parallelogram) Write the area formula for the
(Bottom + Top)⋅ h
1
trapezoid next to the figure.
A=
or A = (Bottom + Top)⋅ h
2
2
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