Question

an architect’s 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?
(image of a coordinate grid with a pentagon drawn, and multiple - choice options: a. about 10 ft, b. about 77 ft, c. about 36 ft, d. about 21 ft)

Explanation:

Step1: Identify Coordinates

Assume each grid square is 1 unit. The vertices of the pentagon (from left to right, bottom to top, etc.) are: \((-6, 0)\), \((-6, 7)\), \((0, 10)\), \((6, 7)\), \((6, 0)\).

Step2: Calculate Horizontal Sides

Bottom side: from \((-6, 0)\) to \((6, 0)\), length is \(6 - (-6) = 12\) ft.

Step3: Calculate Vertical Sides

Left vertical: from \((-6, 0)\) to \((-6, 7)\), length is \(7 - 0 = 7\) ft.
Right vertical: from \((6, 0)\) to \((6, 7)\), length is \(7 - 0 = 7\) ft.

Step4: Calculate Slant Sides

Left slant: from \((-6, 7)\) to \((0, 10)\). Using distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), \(x_2 - x_1 = 0 - (-6) = 6\), \(y_2 - y_1 = 10 - 7 = 3\). So \(d = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.7\) ft.
Right slant: from \((0, 10)\) to \((6, 7)\). Similarly, \(x_2 - x_1 = 6 - 0 = 6\), \(y_2 - y_1 = 7 - 10 = -3\). \(d = \sqrt{6^2 + (-3)^2} = \sqrt{45} \approx 6.7\) ft.

Step5: Sum All Sides

Perimeter = \(12 + 7 + 6.7 + 6.7 + 7\)
= \(12 + 14 + 13.4\)
= \(26 + 13.4 = 39.4\) (close to 36, likely grid size adjustment: maybe each grid is 1 ft, but maybe my coordinate assumption was off. Wait, recheck: maybe the vertical sides are from y=0 to y=7? Wait, the graph: at x=-6, y=0; x=-6, y=7 (since it's at 7 on y-axis? Wait, the y-axis has 0,2,4,6,8,10. So from ( -6,0) to (-6,7): 7 units. From (6,0) to (6,7): 7 units. Bottom: from -6 to 6: 12 units. Left slant: from (-6,7) to (0,10): horizontal distance 6, vertical distance 3. Right slant: same. Then total: 12 + 7 + 7 + 2*sqrt(45) ≈ 12 +14 +13.4 ≈ 39.4, closest to 36 (option C). Maybe my grid was misread: maybe each square is 1 ft, but the vertical sides are 7, slants ~6.7, bottom 12. Sum: 12 +7 +7 +6.7 +6.7 ≈ 39.4, which is about 36 (maybe rounding differences). So the answer is C.

Answer:

C. about 36 ft