COMPARISON OF POLYGON AREAS 3/3

Ech pupil chooses three sheets of origami paper.

A discussion question: Look at your sheets.Do they all have the same measurements? How can you check this? Explain

Answer: By placing one sheet on another and rotating the sheet we find that the lengths of the sides are equal.

Folding instructions: Fold parallel sides of two sheets.

Folding instructions: Fold opposite vertices of the extra sheet.

A discussion question: Compare the sheets that you have folded into a triangle shape and rectangular shape. Are the areas equal? Explain.

Answer: The area of the rectangle is one half the area of the square .

Answer: The area of the triangle shape is one half the area of the square.

Answer:  The areas of both shapes are equal because both the triangle and the rectangle are one half of the original squares.

Folding instructions: Fold opposite parallel shorter sides of both rectangles on to each other.

Folding instructions: Open both folds.

Folding instructions:  On the two rectangles fold the two vertices as shown.

Folding instructions: Open up the folds on one of the rectangles.

A discussion question: What is the area of each one of these triangles? Explain.

Answer: The two triangles together form the shape of a small square having an area of one quarter of the area of the larger square.

Folding instructions: Open out the folds of both vertices.

Folding instructions: Turn over both shapes.

Folding instructions: Fold the vertex as shown.

Folding instructions: Turn over both shapes.

Folding instructions: On both shapes fold fold a vertex to obtain a triangle.

Folding instructions: Hold one vertex in each hand and open out the triangle into the shape of a square.

Folding instructions: Turn over both squares.

Folding instructions: On only one square open out the four triangles.

A discussion question: Fold and open the four triangles and check whether the sum of the areas of these four triangles together is equal to the area of the smaller square made by the folding.

Answer: Folding each of the four triangles onto the smaller square will show that the sum of the areas of the four triangles is equal to the area of the smaller square.

A discussion question: What is the area of the four folded and opened triangles together when compared with the area of the large square and the small square?

Folding instuctions: Fold back the four triangles.

Folding instructions: Open out one of the triangles.

Folding instructions: On both shapes fold the marked triangle as shown.

Folding instructions: On both shapes fold the colored triangle into two parts.

Folding instructions: On both shapes fold the white triangle into the pocket of the colored triangle as shown.

  A pair activity: Join the two triangles together to form the shapes of a triangle and a parallelogram.

A discussion question: Can you compare the areas of the triangle and parallelogram? Explain.

Answer: As each triangle has the same area and both the triangle and parallelogram were formed from two triangles they both have the same area although they are not congruent.

A group activity: Join four triangles together and form the shown polygons.

A discussion question: Can you compare the areas of the square and parallelogram? Explain.

Answer: Although the two polygons are not congruent they were formed with four equal area triangles and the areas of both polygons are equal.

A group activity:Join  triangles together and form the shown polygons.

A discussion question: Can you compare the areas of the rectangle and parallelogram? Explain.

Answer: As all triangles have the same area, the area of the parallelogram formed from two triangles is half the area of the rectangle formed from four triangles.

A pair challenge:With four triangles form two other different polygons  and compare areas.

A concluding question: What have you learnt from this lesson about areas of different polygons?

On the longer side of each triangle there is a pocket. You can put the pages of your book into the pocket.

A bookmark !