The area of a shape is the amount of space it can occupy, while the perimeter is the sum of its sides.
- The value of x is 7.5 ft
- The area of the shape is 57 square feet
Given that:
[tex]P = 39[/tex] --- the perimeter of the shape
The value of x
The perimeter is the sum of all sides.
So, we have:
[tex]P = x + x + 3.5 + 3.5 + 3 + 3 + 9 + (9 - 3.5 - 3.5)[/tex]
Substitute 39 for P
[tex]x + x + 3.5 + 3.5 + 3 + 3 + 9 + (9 - 3.5 - 3.5) = 39[/tex]
[tex]2x + 24 = 39[/tex]
Collect like terms
[tex]2x = -24 + 39[/tex]
[tex]2x = 15[/tex]
Divide through by 2
[tex]x = 7.5[/tex]
The area of the shape
The shape can be divided into two rectangles
- A 9ft by 3ft rectangle
- A (9 - 3.5 - 3.5)ft by x ft rectangle
So, the area of the shape is:
[tex]Area = 9ft \times 3ft + (9 - 3.5 - 3.5)ft \times x ft[/tex]
[tex]Area = 27ft^2 + 2ft \times x ft[/tex]
Substitute [tex]x = 7.5[/tex]
[tex]Area = 27ft^2 + 2ft \times 15 ft[/tex]
[tex]Area = 27ft^2 + 30 ft^2[/tex]
[tex]Area = 57 ft^2[/tex]
Hence, the area of the shape is 57 square feet.
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