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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.

Know:

the dimensions of 2-D shapes such as length and width (height)
the properties of rectangles, triangles and parallelograms.

Understand:

That formulas can be used to quickly find the area of a rectangle, triangle or parallelogram.

Do:

I can find and use the formula for the area of rectangles, triangles and parallelogram to solve problems involving the areas of surfaces.

Elaborations:

building on the understanding of the area of rectangles to develop formulas for the area of triangles
establishing that the area of a triangle is half the area of an appropriate rectangle
using area formulas for rectangles and triangles to solve problems involving areas of surfaces
constructing different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area.
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

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.

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.

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.

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).

Teaching Ideas

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Sample Problems

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Construct three similar rectangles, using grid paper or a geoboard, and compare the perimeters and areas of the rectangles.
Estimate and calculate the area of composite two-dimensional shapes by decomposing into shapes with known area relationships.
Create two different triangles with an area of 12 square units, using a geoboard.
Decompose a rectangle and rearrange the parts to compose a parallelogram with the same area.
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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Area and Perimeter Videos

[/title][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”ECJfSyg_Obo” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”UfUwTtaHyp8″ width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”xz6gBA0M9FY” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”QmUNqVjm4R4″ width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”KVFwRA7kcLY” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”_ROJc1tuOUw” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][fullwidth background_color=”” background_image=”” background_parallax=”none” enable_mobile=”no” parallax_speed=”0.3″ background_repeat=”no-repeat” background_position=”left top” video_url=”” video_aspect_ratio=”16:9″ video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” border_size=”0px” border_color=”” border_style=”” padding_top=”20″ padding_bottom=”20″ padding_left=”0″ padding_right=”0″ hundred_percent=”no” equal_height_columns=”no” hide_on_mobile=”no” menu_anchor=”” class=”” id=””][button link=”http://www.alamandamaths.com/?page_id=1634″ color=”default” size=”” type=”” shape=”” target=”_self” title=”” gradient_colors=”|” gradient_hover_colors=”|” accent_color=”” accent_hover_color=”” bevel_color=”” border_width=”1px” icon=”” icon_position=”left” icon_divider=”no” modal=”” animation_type=”0″ animation_direction=”left” animation_speed=”1″ alignment=”” class=”” id=””]Next Lesson[/button][/fullwidth]

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

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

Know:

the dimensions of 2-D shapes such as length and width (height)

the properties of rectangles, triangles and parallelograms.

Understand:

That formulas can be used to quickly find the area of a rectangle, triangle or parallelogram.

Do:

I can find and use the formula for the area of rectangles, triangles and parallelogram to solve problems involving the areas of surfaces.

Elaborations:

building on the understanding of the area of rectangles to develop formulas for the area of triangles

establishing that the area of a triangle is half the area of an appropriate rectangle

using area formulas for rectangles and triangles to solve problems involving areas of surfaces

constructing different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area.

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

Rectangles, Triangles and Parallelograms

Area of Rectangles

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

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.

Area of Triangles

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

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.

Area of Parallelograms

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

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).

Teaching Ideas

Sample Problems

Construct three similar rectangles, using grid paper or a geoboard, and compare the perimeters and areas of the rectangles.

Estimate and calculate the area of composite two-dimensional shapes by decomposing into shapes with known area relationships.

Create two different triangles with an area of 12 square units, using a geoboard.

Decompose a rectangle and rearrange the parts to compose a parallelogram with the same area.

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

Area and Perimeter Videos