Tilted Square Investigation
In this activity one unit of area is equal to one grid square.
First, complete the quiz below to check your knowledge of finding the area of rectangles and triangles. If you wish to improve your quiz score, press 'start over'. Otherwise, don't press 'start over'.
Remember that a right triangle fills up half of a rectangle.
Drag the red points to make a square that has area 36. Remember that all four sides of a square have equal length and all four angles are equal to 90 degrees.
Drag the red points to make two squares of different sizes. Make the larger square so that it has four times the area of the smaller square.
The quadrilateral below has two fixed points and two movable points. Move the two red points to make a tilted square.
Move the two red points on the shape below to form a tilted square.
Determine the area of one of the green triangles. Type your answer into the box.
Move the four triangles so that they fit onto the outside of the blue square.
The applet below shows one blue tilted square and four green triangles.
Below the applet is an image that shows four right triangles fitted to the sides of the tilted blue square.
Resize and move the green triangles to match the image.
The area of each triangle and the blue square is shown in the figure below.
The side length of the large square is 6. The area of the large square is 6 x 6 = 36. Explain how we calculate that the area of the tilted, blue square = 26.
What is the length of one side of the blue square?
The side length of the large square below is 12 units.
Move the red point to make different sized blue squares.
Develop a method for calculating the area of the blue square. Test your method using different sized blue squares. Use the checkbox to see if your calculations are correct.
Determine how to calculate the side length of the blue square.
Explain your method for calculating the area of the blue square.
Explain your method for calculating the side length of the blue square.