Reasoning to Find Area

Warmup

Activity #1

 Finding Area by Tiling with Unit Squares. 

Tiling, otherwise known as tessellation, is a way of arranging identical plane shapes so that they completely cover an area without overlapping. In this activity, the identical shapes are unit squares. Follow the instructions below to find the area of a shape by tiling.

• Click and drag the squares to fill a figure. ​
• Find its area by the number of enclosed squares.
• Click on to return the tiles.

• Answer the questions below.

Activity #2

 Find the Area of a Rectangle.

The area of a rectangle is generally found by multiplying the length by the width. This can be proven by interacting with the applet below. What ever the dimensions of the rectangle happen to be, the numbers of squares that are enclosed will be the product of the side lengths. Investigate!

• Move the sliders and observe the effect on the dimensions of the figure.
• Count the squares that are enclosed in each case.
• Verify the area by multiplying the measure of the length by the measure of the width.

• Answer the questions below.

Activity #3

Find Area of Irregular Shapes.

Whether a shape is regular or irregular, the number of squares that will cover it with no gaps, is the area of the figure. It may be a little tricky, but the area of irregular shapes can be found.

• Find the area of the shaded portion of the figures. If you wish, you can use the triangles( brown in color), in the second app below to help illustrate and support your explanations for the area of figure D.

• Answer the questions below.

Challenge #1

Find the area of the figure below.

Challenge #2

Find the area of the figure below.

Challenge #3

Find the area of each shaded region. Show your working on the applet using the tool.