Calculating Properties of Shapes		Name:

Use the sketch below to calculate the area of the square. Add all linear dimensions to the sketch that were used in the calculations. Note: Each grid unit = 1 inch.


The area of the square represented above is revised to be 90.0 in.2.  Note that the original grid spacing no longer applies.
a.	What is the side length of the square? Justify your answer.

b.	Using this length, what would be the corresponding grid spacing for the sketch above? Justify your answer.

c.	What size circle would you cut out of the square in order to have a remaining area of 66.5 in.2? Justify your answer.

d.	Apply all necessary annotations and dimensions to size the shapes and locate the circle in the center of the square.

Complete the sketch of the rectangle. It must have an area of 2.25 in.2 Prove the enclosed area by dimensioning the sketch and showing the area calculation. Show only those dimensions needed for the area calculation. Note: Each grid unit = 0.25 inch.
 It is a square with a circle within. Square length is 9 boxes.


Use the sketch below to calculate the area of the rhomboid. Add linear dimensions to the sketch that were used in the area calculation. Note: Each grid unit = 1 inch.
It is 3 boxes wide. It goes 8 inches down. Goes 2 down and 1 left for slope.

Complete the sketch of the obtuse triangle. It must have an area of 1.75 in.2. Prove the geometry by dimensioning the sketch and showing the area calculation. Show only those dimensions needed for the area calculation. Note: Each grid unit = 0.25 inch.

You are given a sheet of cardboard that is 8.0 in. x 11.0 in. How many full circles with a diameter of 3.0 inches can you cut from the cardboard? What is the percentage of waste if the excess cardboard (outside the circles) is thrown away?


An ellipse has an area of 4.71 in.2 and a minor axis that is 2.00 in. long. Solve for the major axis, and then sketch the ellipse using that dimension. Show only those dimensions needed for the area calculation. Note: Each grid unit = 0.25 inch.


What side length would you specify if you were required to create a regular hexagonal plate that was comprised of 33 cm2 of sheet metal? Sketch the hexagon, dimension the side length on the sketch to 0.1 cm, and indicate your grid spacing. Justify your dimension.

Extra Credit
The sketch shown below is for a commercial sign. It was drawn to 1/10 of its true size. What is the area of the actual sign? Prove your answer by showing all calculations. Note that the sign was not drawn to scale but was drawn on a grid in which the grid spacing unit is 1 inch.