A regular polygon<span> is equilateral (it has equal sides) and equiangular (it has equal angles). To find the </span>area<span> of a regular </span>polygon<span>, you use an apothem — a segment that joins the </span>polygon's<span> center to the midpoint of any side and that is perpendicular to that side (segment HM in the following figure is an apothem).</span>
Given:
The triangles DEF is similar to GHF.
The objective is to find a similar ratio of DF/DE.
Explanation:
Using the basic proportionality theorem, for the similar triangles DEF and GHF,
Considering the first two ratios of equation (1),
On interchanging the segments further,
Hence, the required segment in the blanks is GF/GH.
The area (A) of the whole circle is calculated through the formula, A = πd² / 4. Substituting the given diameter, A = π(10 in)² / 4 = 25π in². The area of the top of each piece is 1/6 of the this area. Thus, the answer is approximately 4.17 in².
