Echo loves to sit up high on Amanda’s computer which sits on top of her desk. However, she often reaches down in front and pats the computer, turning Amanda’s computer off right in the middle of her game! So, Amanda has decided to build a bed for Echo. She decides on an octagonal perch because she can use 2 by 4's for the sides of a polygon but she wouldn't be able to for a circle. She has a flat board and 2 by 4’s available to use.
She expects the base and sides to look something like this:
She expects the base and sides to look something like this:
How shall should Amanda cut the base board? What strategy will work well for an octagon?
What shape are the corner cut outs? What would the cutting angle be? The interior angle in the wood?
What shape are the corner cut outs? What would the cutting angle be? The interior angle in the wood?
Timothy previously built a cat tree for Oreo. The tree he built looks like this:
Amanda thinks her cat tree needs to be a little less than two feet across so Oreo has plenty of room. She wants to make a regular octagon with 10 inch long sides. She has a square board large enough to do this.
Where should she mark for cutting? Exactly how large was her board?
Where should she mark for cutting? Exactly how large was her board?
Label a scale model for the base with all side length and angle measures.
Next, she needs to make the sides. Unfortunately for Amanda, Tim either doesn't remember the angle he used to cut the pieces for the sides for Oreo's cat tree or just doesn't want to help his sister today, so she needs to figure it out for herself.
What angle does she need to cut the side pieces at so they all fit together nicely?
Hint: First you need to decide if the go on or around the base! Justify your choice.
Make a scale model of the side pieces including all length and angle measures.
What is the area available for Echo to sleep?
Next, she needs to make the sides. Unfortunately for Amanda, Tim either doesn't remember the angle he used to cut the pieces for the sides for Oreo's cat tree or just doesn't want to help his sister today, so she needs to figure it out for herself.
What angle does she need to cut the side pieces at so they all fit together nicely?
Hint: First you need to decide if the go on or around the base! Justify your choice.
Make a scale model of the side pieces including all length and angle measures.
What is the area available for Echo to sleep?
Part 2
Amanda's best friend, Robyn, also has a cat. She wants Amanda's to help her make a cat tree for her cat. However, she doesn't want hers to be exactly the same. She wants a hexagonal base. How would you cut a hexagon from a 20 inch circular board?
Make a scale model of the base and a side piece with all side lengths and angle measures listed. What is the area available for cat sleeping in Robyn's cat tree?
Amanda's best friend, Robyn, also has a cat. She wants Amanda's to help her make a cat tree for her cat. However, she doesn't want hers to be exactly the same. She wants a hexagonal base. How would you cut a hexagon from a 20 inch circular board?
Make a scale model of the base and a side piece with all side lengths and angle measures listed. What is the area available for cat sleeping in Robyn's cat tree?
Part 3
What other bases could you use? Choose one and make the scale model above. How much available area is there with your base?
What other bases could you use? Choose one and make the scale model above. How much available area is there with your base?