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Area Madness!!! Mrs. Poppell’s class
Crazy old Dr. Williams is a mad scientist that has found the secret formula for taking over the world. He knows you are coming to stop him, so he set out some booby traps to catch you. It’s up to you to find the answers to these problems and keep him from controlling the world, good luck!!
After traveling all day, you finally find the home of Dr. Williams. It’s getting dark, better hurry and get inside!!
As you come to the door, you hear a voice over the crackly intercom. “Ah, I see you’ve finally found me. You’ll never get through the door though!” He cackles, “You can’t open the door unless you know the code, and I’ll never tell you that the key to the code is to find the area of the door, which is ten feet high and six feet wide. Oops.” The evil doctor unwittingly gave you the key to cracking the code! All you have to do is find the area of this door and punch the number into the keypad to the left.
Whew! You made it inside before it started to rain. Outside, the thunder is getting closer and you can see the flashes of lightning through the dirty windows. As you walk further inside the house, you stumble upon a table with three round bowls on it. There is a note on the table, stuck under one of the bowls.
Dear Children. I see that you have made it through my first obstacle with no difficulty, however, you will never figure this one out. This table holds three bowls, each a different size. The diameter of the smallest bowl is 8 inches across. Each bowl under it increases in diameter by 2 inches as you go down. If you can find the area of each of the circles created by my bowls, I will graciously allow you to come upstairs to my lab. If not, however, you will find yourself in the dungeon, with my pet, Fluffy. Do not let the name fool you, I can assure you that Fluffy loves children. Loves to eat them. Good luck, you’ll need it. Ha Ha Ha! Dr. Williams
8 in. Uh-oh. It’s a good thing we remembered the formula for finding the area of a circle. So, if the smallest bowl has a diameter of 8 inches, that means the length of the radius is…
4 ? Oh, yeah. The length of the radius is 4 inches. Now, to find the radius of the other two circles, we have to remember what that crazy old man said in his note. “Each bowl increases in diameter by two inches as you go down.” So that means that the next to largest bowl has a diameter of…
4 10 Right, ten inches. That means that the radius of this circle is five inches. Now to find the diameter of the last circle, we have to add two to the number we found for the middle circle. That gives us…12. So, we have a circle with a radius of 4 inches, a circle with a radius of 5 inches, and finally a circle with a radius of…
4 5 6 Ah, yes. 6 inches. So, now that we have the radius lengths for each circle, we can work on finding the area of each of them. Uh-oh, better hurry, I think I hear Fluffy barking down below!
50.24 78.5 113.04 Great job! Now that we have found the area of the circles, we can begin our ascent to the evil scientist’s laboratory! Now, where are the stairs?
Just beyond the table with the bowls, we see the staircase. As we make our way toward them, an angry voice echoes throughout the house. “What?!? You mean to tell me that a bunch of fifth graders actually solved the problem?? Well, I’ll show them! They’ll never get around the pit of lava upstairs!!” Great! Just when we think we have him, he mentions a pit of lava? Maybe we should just turn around and let him take over the world.
Okay, okay. We trudge up the stairs nervously, each step creaking ominously. When we get to the top, there is a long hallway stretched out in front of us. At the end, there is a single door. This must be where Dr. Williams makes up his crazy schemes.
We enter the open door carefully, looking all around so we don’t fall into the lava pit. Ah-ha. There it is. How are we supposed to get around this thing? There is a keypad next to the open door, but how are we supposed to measure it?
Cool, someone left a tape measure on the floor next to the scalding hot pit of fire. Quick, someone, pick that thing up and lets measure this thing!! Don’t look at me, I’m not picking it up. Oh, okay. I guess I’ll have to since no-one else will. Hmmph.
I pick up the tape measure and hand it to one of you. If I had to pick it up, I’m not walking near that thing to measure it. Oh, alright. I suppose I’ll have to do it.
24 ft. 30 ft. Okay. I did it. I measured the pit of lava. But you guys are going to have to figure this one out on your own. I’m exhausted. And a little sweaty.
Great job. Now let’s enter it into the keypad. 7-2-0. Wow, look what happened! There’s a walkway across the lava pit now. Let’s go get that mad scientist!
We walk carefully across the metal walkway and safely reach the other side, to another door. This could be it, we’re almost there!
Someone cackles as we get closer to the door. We step through slowly and to our surprise…There’s no one in here! All that we see before us is a few ladders and a triangle painted on the wall. When we look up, we can see Dr. Williams white hair poking out from a hole in the ceiling. “I can see that you made it through the pit of lava, but you’ll never figure this one out! What you see before you is a triangle with an area of 12 square feet. If you can figure out which ladder to use before I make my escape, I will relinquish my plans to take over the world. If not, well, let’s just say that Fluffy would have been much more fun!” He disappears, leaving us to try and figure out which ladder will reach the top first.
Area=12 Square Feet Did anyone happen to bring the tape measure with them?
Great! Now, Dr. Williams said that the area of the triangle is 12 square feet. How would we find the height of the ladder to use? The first thing we should do is measure the base of the triangle. Area=12 Square Feet
Area=12 Square Feet 4 feet So…the length of the base is 4 feet. Now how do we find the height quickly? If the area of a triangle is one half of the base times the height, let’s do some quick thinking.
Let’s start by putting what we know into an equation. A= ½ (BxH) We know that the area is 12 and the base is 4, now what?
We need to find a six foot ladder. Then we can stop Dr. Williams for good!
Hold it right there! We’ve come to stop your evil plans. Don’t even think about getting on that rocket!!
“You’re too late! The world is mine! As soon as I find my briefcase.” We take a step toward his and he dashes to the rocket ship. “Err, I’ll just be leaving now. Mark my words, one day the world will be mine. Until we meet again!” He gets into the rocket and it blasts off, blowing a hole through the roof. I guess he didn’t really think that one through.
Looks like he forgot the secret to taking over the world. He left his briefcase here. Well, at least that’s over with. I hope that’s the last time we see that crazy old man. Thanks guys, I appreciate all the help!
The End Or is it?