2.7: Body Surface Area

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Surface area (A) is an important feature of the human body. Surface area affects the rate at which heat transfers into or out of the body and the rate at which certain chemicals can be absorbed through the skin. The severity of burn injuries depends on the degree of the burn, but also on the percentage of total body surface area affected^[1]. The areas and surface areas of geometric shapes can be found using various formulas, such as quicklatex.com-300c580b90d98bd69bf1ae2c03831a6d_l3.png for triangles. The surface area of a convoluted shape such as the human body is difficult to measure, but we can use typical ratios (proportions) to quickly approximate body surface area. For example the palm surface area can be easily measured as quicklatex.com-17e38d1a27422449948269d681d651e1_l3.png and the ratio of palm surface area to body surface area is typically 1/200, which might also be written as 1:200, 0.005, or 0.5%^[2]. The units of area will be length units squared, such as square meters (meters squared or m²). We need to be careful when converting units involving powers (squared, cubed, etc.) and the chain-link method allows us to make sure our units cancel correctly.

Example \(\PageIndex{1}\): Example square inches to square feet.

We are going to replace the carpet in a room. Carpet is sold by the square foot, so we are trying to determine the square footage of carpet in room. We use a measuring tape and find out that the room is 148 in long by 108 in wide. Multiplying length by width we get 15,984 in². To convert to feet we need to multiply by the conversion factor twice in order to cancel the squared unit:

\[15,984 \mathrm{in}^{2}=15,984 ; \pi \cdot j \pi\left(\frac{1 \mathrm{ft}}{12 \mathrm{in}}\right)\left(\frac{1 \mathrm{ft}}{12 \mathrm{in}}\right)\]

quicklatex.com-12916f64e5bdf7db3b7767ef20d02c0b_l3.png — Figure: Multiplying across the top and bottom we have:

\[15,984 \mathrm{in}^{2}=15,984\left(\frac{1 \mathrm{ft}^{2}}{144}\right)=111 \mathrm{ft}^{2}\nonumber\]

Reinforcement Activity

Measure your palm length and width in units of cm. Then calculate your palm surface area in units of cm². Next, calculate your approximate body surface area in units of cm². Finally use the chain-link method to convert your body surface area to both square inches (in²) and m².