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MEASUREMENT MISSIONS. CONFIDENTIAL FILES: AUTHORIZED PERSONELL ONLY. Dear Students,

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I am in dire need of you help! You see, I have spent my entire life producing blueprints and taking measurements all across the country. As a Secret Agent of Measurement, it is my job to make sure the town has correct measurements on file for new buildings and other construction. This is important information for the government to have, but we wouldn’t want it to get into the wrong hands. I am requesting your help in solving a few of our top priority cases. I am currently on a mission in Paris dealing with the Eiffel Tower and will not return to the United States before these files are due to the President. Rumor has it that your class in one of the brightest groups around. If you choose to help me, you will get to see some of the towns most top secret architecture files. You’ll even get to create some files of your own. Remember, these files are top secret and not everybody gets to see them. If you become a Master of Measurement you will be among the few certified CIAgents of Measurements. Then you can help calculate problems across the world!

Sincerely,

Secret Agent P. Rimeter

MISSION ACCEPTED

20 m

The Washington Monument

The Washington Monument stands 169 m tall and 20m wide. It consists of four, flat, rectangular sides. An earthquake has architects worried about the stability of the monument. They advise reinforcements be installed along the length of all four sides on each rectangular face. How many meters of reinforcement material are needed for one rectangular face? How many meters are needed for all four faces together?

- How do we find the distance around a rectangle?
- Perimeter is the total distance
- around a polygon. We add the
- lengths of each of the sides to
- determine the total distance.
- If the Washington Monument is 169m tall and 20m wide…

169m + 20m + 169m + 20m = ?

(We’re adding 4 sides so we have to make sure we have four measurements)

The perimeter of one face is 378m.

What about for all four faces together?

169m

20m

70 yd

80 yd

The Egyptian Pyramids

An international museum wants to create an exact replica of the Egyptian Pyramids. In order to do so, they need the measurements along each edge of the pyramid. Each face of the pyramid is identical. What is the perimeter of a single triangular face? If there are four equal faces, what is the total perimeter around all three?

- How do you find the perimeter of a triangle?
- How could you use the information you’ve been given to determine the perimeter for each of the four faces?
- If there are four faces, what is the total perimeter for each of them combined?

70yd + 70yd + 80yd = ?

220yd + 220yd + 220 = ?

220yd * 4 faces = ?

If we add the perimeters this way or multiply them by the number of faces, are we actually calculating the same face twice?

25ft

70 ft

100 ft

50 ft

The TajMahal

Finally, the arches of the TajMahal need to be repainted. In order to begin repainting the trim around each arch, we must know the exact distance around the edge of each arch as well as the total length that needs to be painted. Each of the smaller arches are congruent to one another. We can find the perimeter of any polygon. However, a polygon cannot contain curved sides. How can we use only polygons to determine the perimeter of each arch?

- The TajMahal
- What is the sum of the perimeters of the nine main arches?
- How could you determine the lengths of each side even though they were not given to you?
- Did it matter that we used triangles and rectangles?
- Did the fact that so many of the arches were congruent make the problem easier or harder to solve?

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