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The Rectangle Method Finding Area of Triangles and Parallelograms

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A 30 Second Look-See Find something in the room shaped like: a hexagonal prism a cylinder a quadrangle a cube

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Math Journal page 315 Read the top of page 315 Your job will be to think of ways to find the areas of the triangles – I am not interested in the answer. I am interested in the methods you and your partner discover.

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Rectangle Method This is called the rectangle method because rectangles are used to surround the figure or parts of the figure. All of the areas that are calculated are either areas of rectangles or of triangular halves of rectangular regions.

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Add the Parts

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Split this triangle up into two different triangles, both with right angles, count the units that cover each and find the sum of the two parts.

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3 units 12 units

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3 units + 12 units = 15 units 3 units 12 units

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Using the rectangle method, draw a rectangle around each of these triangles.

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What observation can you make about these shapes and the shaded regions?

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These triangles and ½ of the area of the rectangle. How will this information help us to find the area of the triangles?

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3 units 12 units

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Find the area of this triangle with your table.

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Find the area of each rectangle by multiplying the base x height. 9 units 15 units

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To find the area of the triangles divide the area of the rectangles by 2 or find the value of ½ the rectangle. 9 ÷ 2 = 4 ½ units 15 ÷ 2 = 7 ½ units

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4 ½ + 7 ½ = 12 units 4 ½ units 7 ½ units

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Review your work Return to page 315. Find the area of triangle #1 by splitting the triangle into two right triangles. Use the add the parts method to find the area of the complete triangle.

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To find the area, draw two right angles around the triangle to create a rectangle.

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Find the area of the yellow and blue triangles. Use the rectangle method mentally.

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7 ½ units 5 units

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The sum of the yellow and blue triangles is 12 ½ units.

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To find the area of the red triangle, find the area of the rectangle and subtract the 12 ½ units of the blue and yellow triangles. The difference will be the area of the red triangle.

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If the yellow triangle is 7 ½ units, and the blue triangle is 5 units, does it make sense that the red triangle is 2 ½ units? 15 units – 12 ½ units = 2 ½ units.

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Review your work

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Area of a Parallelogram

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Use what you know to determine a strategy to find the area of this shape.

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Determine the areas of the three shapes and add the parts.

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1 x 6 = 6 6 ÷ 2 = 3 = 3 units

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Determine the areas of the three shapes and add the parts. 1 x 6 = 6 6 ÷ 2 = 3 = 3 units

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Determine the areas of the three shapes and add the parts. 6 x 4 = 24 units

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3 + 3 + 24 = 30 units = 3 units 24 units = 3 units

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Review your work Return to page 315. Find the area of triangle #3 by splitting the parallelogram into two right triangles and a rectangle. Use the add the parts method to find the area of the complete parallelogram.

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Practice with a Partner Math Journal page 316

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Practice on Your Own Math Sheet p. 126

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