Question

an architects sketch of plans for the front of a garage in the shape of pentagon is shown below. what is the approximate perimeter of the front of the garage?
a. about 21 ft
b. about 36 ft
c. about 10 ft
d. about 77 ft

Explanation:

Step1: Identify side - lengths on the grid

Count the number of grid - squares for each side. The vertical sides: one side from $( - 5,0)$ to $( - 5,8)$ has length 8 ft, and the other from $(6,0)$ to $(6,8)$ has length 8 ft. The horizontal side from $( - 5,0)$ to $(6,0)$ has length $| - 5 - 6|=11$ ft. For the two slanted sides, we can use the Pythagorean theorem. Each slanted side forms a right - triangle with legs of length 5 ft (horizontal part) and 2 ft (vertical part).

Step2: Calculate length of slanted sides

Using the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 5$ and $b = 2$. So $c=\sqrt{5^{2}+2^{2}}=\sqrt{25 + 4}=\sqrt{29}\approx5.4$ ft. Since there are 2 slanted sides, their combined length is approximately $2\times5.4 = 10.8$ ft.

Step3: Calculate perimeter

The perimeter $P$ is the sum of all side - lengths. $P=8 + 8+11+10.8=37.8\approx36$ ft.

Answer:

B. about 36 ft