Architectural Drawing and
Calculations
Some of the great architectural designs began as mathematical drawings. Mathematical
drawings are used by architects, community planners, builders, and landscapers, to
name a few. As you work through this task, you will use mathematical drawings to apply
your knowledge of the Pythagorean theorem and irrational numbers to develop
landscaping plans and to help plan events for the brand new Mission Viejo Park.
As you complete the task, keep these questions in mind: How can you use the
Pythagorean theorem to determine the length of the garden walk our new park? How
are irrational numbers used in building a garden walkway?
Directions:
Complete each of the following tasks, reading the directions carefully as you go.
You will be graded on the work you show, or your solution process, in addition to your
answers. Make sure to show all of your work and to answer each question as you
complete the task. You can type your work into this document or write it. When
completed submit to me for a grade. You will be given partial credit based on the work
you show and the completeness and accuracy of your explanations.
Now let’s get started!
Step 1: Exploring the Pythagorean Theorem
On the southeast corner of the Mission Viejo Park, there is a garden walk. It is marked
off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row
along which flowers will be planted.
a) If side a measures 90 feet and side b measures 120 feet, how many feet of
flowers will be planted along side c, the hypotenuse of the triangle? Show your work
and explain your reasoning. (2 points)
b) Calculate the area of the red triangle to find the area of the garden. Show your
work. (2 points)
c) Mission Viejo has an outdoor concert theater. Before a concert, the area reserved
for special seating is roped off in the shape of a triangle as shown below. How can
the converse of the Pythagorean theorem help you determine whether the roped off
area is in the shape of a right triangle? (2 points)
d) The front of the stage, side C, is 50 feet long. A 40-foot rope runs along the side
of square B. A 30-foot rope runs along the side of square A. Is the roped off area,
triangle ABC, a right triangle? Explain. (2 points)
e) The diagonal of square A, marked off by the red stars, is where the concession stand
is located. A local high school band is performing at the outdoor theater on a
summer evening. The band has a school banner that is 40-feet long, and band
members would like to hang it across the concession stand to let people know they
are performing. Estimate the length of the concession stand to determine if the
school banner can fit across the length of the concession stand. Show your work
and explain your reasoning. (2 points)
Step 2: Finding distance on the coordinate grid
a) This is a blueprint drawing of the stage area at Mission Viejo. The length of one
square on the grid is equal to 5 feet. According to the blueprint, the length of the
diagonal of square C is 60 feet. Is that correct? Explain. (2 points).
b) If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for
the corners labeled with red stars, would that be an accurate representation of the
length of the diagonal of the square C? Show your work and explain your reasoning.
(4 points—2 points for finding the length of the diagonal; 2 points for explanation)
Step 3: Using the Pythagorean theorem to find the unknown
At another park in Mission Viejo, neighbors get together to plan a community garden.
Plans for the community garden are shown below.
a) The members of the gardening group plan to build a walkway through the garden as
formed by the hypotenuse of each of the four triangles in the drawing. That way, the
gardeners will be able to access all sections of the garden. Calculate the length of
the entire walkway to the nearest hundredth of a yard. Show your work. (4 points—1
point for each length calculation and 1 point for the total distance)
b)
Is the value you just wrote for the total length of the walkway a rational or
irrational number? Explain. (2 points)
c)
The group is planning to build a fence around the garden. How many yards of
fencing materials do they need for the fence? Show your work. (3 points—2 points for
finding the value of side b and 1 point for finding the perimeter of the garden)