A client wants a new patio that surrounds a koi pond the exa

A client wants a new patio that surrounds a koi pond (the exact design is on the page). The client likes symmetry and the number 7. The design is made of circles. triangles, and squares. The circles have the radius 7 feet including the koi pond. The start is create by connecting 8 isoscelles right triangles with length both being 7 ft long. Steps creating a patio: Step 1: stake and pain the perimeter, Step 2: Fix the patio height, Step:3 Excavate and Tamp, Step 4: Protect from invasion (fabric) doesnt include pond, Step 5: Fill in the gravel (heights of 1 inc) does not include pind, Step 6: lay down sand (height of 1 inch) doesnt include pond, Step 7: Screed Sand, Step 8: Add edging, Step 9: Snap a chalk line and place pavers, and Step 10: Cut odd pieces.

a) what is the total area of the patio-with the kio pond

b) what is the area of the patio withou the kio pond

c) what is the area that each of the materials cover

d) how many units of each material must be ordered

e) how much will it cost to order each of the materials

f) the total amount that all of the materials will cost

Solution

a) The patio will be a square. Side is given by diameter of pond (2r) + (1/2*2r + r)2 for left and right = 6r

Area = 22/7 * 36 * 49 = 5544 sq feet

b) Area of pation without Koi pond = Area pf pation - Aread of pond = 5544 - 154 = 5390

c) Area of Bond Stones = 42*1 * 3 = 126 sq ft,

Area of White Stones = 3 Circles + 4 right triangles with base = 2r and height = r

                                 = 3* 154 + 4 * 49 = 462 + 196 = 658

Area of Red Stones = 5390 - 658 = 4732 sq ft