The area of the garden box is 42³/₄ feet² = 42,75 feet²
Further explanation
To solve the above questions, we need to recall some of the formulas as follows:
Area of Square = (Length of Side)²
Perimeter of Square = 4 × (Length of Side)
Area of Rectangle = Length × Width
Perimeter of Rectangle = 2 × ( Length + Width )
Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Rhombus = 4 × ( Length of Side )
Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )
Let us now tackle the problem !
Given:
Perimeter = P = 27 ¹/₂ feet
Length = L = 9 feet
Unknown:
Area = ?
Solution:
First we calculate the width of the garden box
[tex]\texttt{Perimeter} = 2 \times ( \texttt{Length + Width} )[/tex]
[tex]27\frac{1}{2} = 2 \times ( 9 + \texttt{Width} )[/tex]
[tex]27\frac{1}{2} \div 2 = ( 9 + \texttt{Width} )[/tex]
[tex]13\frac{3}{4} = 9 + \texttt{Width}[/tex]
[tex]\texttt{Width} = 13\frac{3}{4} - 9[/tex]
[tex]\texttt{Width} = \boxed {4\frac{3}{4} ~ \texttt{feet}}[/tex]
Finally we can calculate the area of the garden box
[tex]\texttt{Area} = \texttt{Length} \times \texttt{Width}[/tex]
[tex]\texttt{Area} = 9 \times 4\frac{3}{4}[/tex]
[tex]\texttt{Area} = \boxed {42\frac{3}{4} ~ \texttt{feet}^2}[/tex]
Learn more
- The perimeter of a polygon : https://brainly.com/question/6361596
- The perimeter of a rectangle : https://brainly.com/question/7619923
- The perimeter of a triangle : https://brainly.com/question/2299951
Answer details
Grade: College
Subject: Mathematics
Chapter: Two Dimensional Figures
Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width
