Question

What is the area in square meters of a \[{\text{100}}\,{\text{ft}}\,\, \times \,\,\,{\text{150}}\,{\text{ft}}\] rectangular yard?

Answer 1

Hint: The number of square units within a polygon determines its area. Consider the difference between perimeter and area as the length of fence required to enclose the yard, while area refers to the space inside the yard. Perimeter is a one-dimensional unit that can be measured in inches, centimeters, or meters. Area is a two-dimensional concept with a length and width. Square units such as square inches, square feet, and square meters are used to measure area. Multiply the length by the width to get the area of a rectangle.

Formula used:
$A = L \times W$, where A denotes field, L denotes length, W denotes width, and $\times$ denotes multiply.

Complete step by step solution:
Our first move is to change the rectangle's lengths from feet to meters. There are \[3.281\] feet in \[1\] meter (i.e.\[{\text{1}}\,{\text{m = 3}}{\text{.281}}\,{\text{ft}}\]).
Given rectangular yard dimensions are as shown below:

So in the next step, we are finding the length of the rectangle,
Length = \[{\text{100}}\,{\text{ft}}\, \times \,\dfrac{{{\text{1}}\,{\text{m}}}}{{{\text{3}}{\text{.281}}\,{\text{ft}}}}\,{\text{ = }}\,{\text{30}}{\text{.5}}\,{\text{m}}\]
Now we are calculating the width as follows,
Width = \[{\text{150}}\,{\text{ft}}\, \times \,\dfrac{{{\text{1}}\,{\text{m}}}}{{{\text{3}}{\text{.281}}\,{\text{ft}}}}\,{\text{ = 45}}{\text{.7}}\,{\text{m}}\]
Now it is the time to calculate the Area,
Area = length x width
Area = \[{\text{30}}{\text{.5}}\,{\text{m}}\,\, \times \,\,{\text{45}}{\text{.7}}\,{\text{m}}\]
Area = \[{\text{1,394}}\,{{\text{m}}^{\text{2}}}\]
So we found that the area in square meters of a \[{\text{100}}\,{\text{ft}}\,\, \times \,\,\,{\text{150}}\,{\text{ft}}\] rectangular yard is\[{\text{1,394}}\,{{\text{m}}^{\text{2}}}\].

Note:
In order to find the area of a rectangle, we should find the length and width of the rectangle. So from the hints given in the question as \[{\text{100}}\,{\text{ft}}\,\, \times \,\,\,{\text{150}}\,{\text{ft}}\] rectangular yard, we firstly found the respective length and width in meters. We changed the rectangle’s length from feet to meters as we want to find the area in square meters. Then from the given equation of area, we substituted the actual values of length and width and found the area.