Question

A skate park consists of two adjacent rectangular regions. What is the perimeter and the area of the park?

Dimensions are 17 yds (length), 4 yd (length), 9 yd (width). 4 yd (width).​

Answer 1

The total perimeter of the skate park is 60 yards, and the total area is 104 square yards.

Step-by-step explanation:

To determine the perimeter and the area of the skate park, which consists of two adjacent rectangles, we need to add the dimensions together accordingly. Since we know the lengths and widths of two rectangles, which are 17 yds, 4 yds (for the first rectangle) and 9 yds, 4 yds (for the second rectangle), we can calculate the total perimeter and area of the skate park.

Firstly, let's find the perimeter for each rectangle and then total them:

• 
  
• Perimeter of the first rectangle: P1 = 2(17 yds) + 2(4 yds) = 34 yds + 8 yds = 42 yds
• 
  
• Perimeter of the second rectangle: P2 = 2(9 yds) + 2(4 yds) = 18 yds + 8 yds = 26 yds

Since the rectangles are adjacent to each other, they share one side each of 4 yds (which gets counted twice in the sum of their individual perimeters). Therefore, we must subtract this shared length twice:

Total Perimeter = P1 + P2 - 2(4 yds) = 42 yds + 26 yds - 8 yds = 60 yds

Next, let's calculate the total area:

• 
  
• Area of the first rectangle: A1 = 17 yds × 4 yds = 68 yds2
• 
  
• Area of the second rectangle: A2 = 9 yds × 4 yds = 36 yds2

Total Area = A1 + A2 = 68 yds2 + 36 yds2 = 104 yds2

Answer 2

Part 1) The perimeter of the park is
`P=52\ yd`

Part 2) The area of the park is
`A=137\ yd^2`

Step-by-step explanation:

see the attached figure to better understand the problem

Part 1) Find the perimeter pf the park

we know that

The perimeter of the figure is the sum of its six length sides (see the figure)

so

`P=17+5+4+4+(17-4)+9\\P=52\ yd`

Part 2) Find the area of the park

The area of the park is equal to the area of two rectangles

The area of rectangle is equal to

`A=bh`

substitute the values

`A=13(9)+4(5)`

`A=117+20`

`A=137\ yd^2`