How many square inches does an 11" x 13" area encompass?

Mathematics

1 answer:

Kryger [21]4 years ago

5 0

The answer to this is 143".

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1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) $\pi=\frac{c}{d}$ , where c is the circumference of a circle and d is its diameter

(2) $A=\pi r^2$ , where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) $d=2r \rightarrow r=\frac{d}{2}$ .

We can rearrange equation (1) to put d in terms of π and c, giving us (4) $d = \frac{c}{\pi}$ , and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

$A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}$