Question

A flower garden measures 14cm by 20cm. There is a path 2m wide all round it. Find the area of the path.​

Answer 1

152 m²

Explanation:

Area of flower garden

Assuming the flower garden is rectangular and its dimensions are measured in meters:

• width of garden = 14 m
• length of garden = 20 m

`\begin{aligned}\textsf{Area of a rectangle} & = \sf width * length\\\implies \textsf{Area of flower garden} & = \sf 14 * 20\\& = \sf 280\:\:m^2 \end{aligned}`

Total area of path and garden

If there is a 2 m wide path all around the garden, the dimensions of the total area will be the dimensions of the garden extended by 4 m:

• width = 14 m + 2 m + 2 m = 18 m
• length = 20 m + 2 m + 2 m = 24 m

`\begin{aligned}\textsf{Area of a rectangle} & = \sf width * length\\\implies \textsf{Total area} & = \sf 18 * 24\\& = \sf 432\:\:m^2 \end{aligned}`

Area of path

To calculate the area of the path, subtract the area of the garden from the total area:

`\begin{aligned}\implies \textsf{Area of path} & = \sf Total\:area-Area\:of\:garden\\& = \sf 432-280\\& = \sf 152\:\:m^2 \end{aligned}`