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Problem 550

A circle is inscribed in an equilateral triangle, whose side is 12\. Find, to the nearest integer, the difference between the area of the triangle and the area of the circle. (Use \(\pi=3.14\) and \(\sqrt{3}=1.73 .\) )

Expert verified

The area of the equilateral triangle is approximately 72.03, and the area of the inscribed circle is approximately 37.81. The difference between the areas is about 34.22, which, when rounded to the nearest integer, is 34.

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Chapter 29

A side of a regular hexagon is 8 inches in length. (a) Find the length of the apothem of the hexagon. (b) Find the area of the hexagon. [Answers may be left in radical form.]

Chapter 29

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Chapter 29

By how much does the area of the circumscribed circle exceed the area of the inscribed circle of a square of side 8 .

Chapter 29

Find the area of a regular hexagon circumscribed about a circle of radius \(\mathrm{r}\). Calculate the area explicitly if a) \(\mathrm{r}=4\); b) \(\mathrm{r}=9\) c) \(\mathrm{r}=16\) d) \(\mathrm{r}=25\).

Chapter 29

The area of pentagon \(\mathrm{ABCDE}\) is \(18 \mathrm{sq}\). in.; the area of a similar pentagon $\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime} \mathrm{D}^{\prime} \mathrm{E}^{\prime}\( is \)32 \mathrm{sq}$. in. The diagonal \(\mathrm{AC}\) is 6 in.; find the length of $\mathrm{A}^{\prime} \mathrm{C}^{\prime}$.

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