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## Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258)

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# LO: To find the formula for the area of rectangles, triangles and parallelograms.

### Elaborations:

• #### Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.

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## Rectangles, Triangles and Parallelograms

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## Area of Rectangles

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#### Finding the area of rectangles is easy, all you have to do is multiply the length by the width.

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#### Another way of finding the area of a rectangle is using an array. An array means using rows and then adding it all up. If each row has 18 squares, if we have 6 rows, we would then go 6 x 18 which is 108 squares in total.

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## Area of Triangles

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#### Finding the area of triangles is easy, all you have to do is multiply the base by the height and half the answer.

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#### The reason for that is that is if I go base x height (or length x width) that is the same formula as the area of a rectangle. If you look at the picture below each of the triangles is only half of the size of a rectangle, which is why the formula is 1/2 x b x h.

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## Area of Parallelograms

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#### Finding the area of parallelograms is easy, all you have to do is multiply the base by the height.

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#### The reason for that is that is if I cut the end piece of the parallelogram, I can slide it to the opposite side and create a rectangle. The area of a parallelogram is the exact same as the area of a rectangle, which is length x width (or base x height).

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## Sample Problems

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• #### Decompose a parallelogram into two congruent triangles, and compare the area of one of the triangles with the area of the parallelogram.

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