Question

directions: study the figure, read each question, and choose the best answer

1. the figure represents the fenced section of ruas yard. what is the perimeter of the fenced section of ruas yard?

a. 200 ft
b. 260 ft
c. 280 ft
d. 320 ft

1. what is the area of the fenced section of ruas yard?

a. 2,400 ft²
b. 2,800 ft²
c. 3,200 ft²
d. 4,000 ft²

Explanation:

Step1: Calculate the perimeter

The perimeter of a shape is the sum of all its sides. For this irregular shape, we can use the property that we can "shift" the inner sides to form a rectangle. The formula for the perimeter of a rectangle is \(P = 2\times(\text{length}+\text{width})\). Here, the length is \(100\) ft and the width is \(40\) ft. But we also have two additional \(20\) ft sides (from the "indentations" which when considered for perimeter add \(2\times20\)).

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Step2: Calculate the area

We can split the shape into three rectangles.

• First rectangle: \(20\times20\) (area \(A_1=20\times20 = 400\) \(ft^2\))
• Second rectangle: \((100-(20 + 20))\times40=(100 - 40)\times40=60\times40 = 2400\) \(ft^2\)
• Third rectangle: \(20\times20\) (area \(A_3=20\times20 = 400\) \(ft^2\))

The total area \(A=A_1+A_2+A_3\)

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Answer:

1. D. \(320\) ft
2. C. \(3,200\) \(ft^2\)