14.5 Areas in Real Life
A standard notebook cover measures about 18\text{ cm} \times 24\text{ cm}, so its area is
18 \times 24 = 432 \text{ cm}^2.
How many such covers would blanket your study table? Estimating real surfaces like this sharpens your feel for size.
Furniture is often measured in inches and feet:
1\text{ in} = 2.54\text{ cm}, \qquad 1\text{ ft} = 12\text{ in}.
To convert areas, we square the length conversion. One square inch is a 2.54\text{ cm} \times 2.54\text{ cm} square:
1\text{ in}^2 = (2.54)^2 \text{ cm}^2 = 6.4516 \text{ cm}^2.
So 16\text{ in}^2 = 16 \times 6.4516 = 103.2256\text{ cm}^2, and going the other way, 232.2576\text{ cm}^2 = \tfrac{232.2576}{6.4516}\text{ in}^2 = 36\text{ in}^2. Similarly 1\text{ ft}^2 = 12^2 = 144\text{ in}^2, and 1\text{ km}^2 = (1000)^2 = 1{,}000{,}000\text{ m}^2.
Squaring the Conversion When you convert a length, the conversion factor appears once; when you convert an area, it appears twice (it gets squared). For example 1\text{ ft} = 12\text{ in} but 1\text{ ft}^2 = 12^2 = 144\text{ in}^2. Forgetting to square the factor is the most common area-conversion slip.
Worked Example
A floor is laid out as an L-shape: a full rectangle 9\text{ m} \times 6\text{ m} with a rectangular notch of 4\text{ m} \times 3\text{ m} removed from one corner. Find the floor area.
Treat the L as a big rectangle minus the missing corner:
\text{Area} = (9 \times 6) - (4 \times 3) = 54 - 12 = 42 \text{ m}^2.
Composite shapes like this are handled by adding and subtracting rectangles (and triangles).
Large pieces of land are measured in acres: 1\text{ acre} = 43{,}560\text{ ft}^2. Across India many local measures are still in daily use, bigha, gaj, katha, dhur, cent, ankanam and others. Very large regions (towns, districts) are sized in square kilometres (\text{km}^2).
Try This Find out the local unit of area used where you live, and how many square metres it equals. Then estimate the area of your classroom, your school, and your town, and look up the actual figures to compare. Which Indian city has the largest area? Which has the smallest?
A widget: the all-shapes area calculator
Use this little calculator to find the area of a triangle, parallelogram, rhombus or trapezium from its measurements.
A widget: unit-square area counter
Pick a length and width (in whole centimetres) and watch the rectangle fill with unit squares, confirming that the count equals length times width.