Find the area of the the regular polygon.

Area of regular polygon: ( About ) 442.8 units^2; Option C

Step-by-step explanation:

~ In this situation we can apply the formula 1/2 * a * P, provided a ⇒ apothem, and P ⇒ Perimeter of the shape ~

Here we are directly provided with the apothem, which makes it a whole lot easier than dividing the figure into triangles, drawing an altitude to one of the triangles, determining the tan degree of the triangle etc.

1. Given one of the sides to be 11 units, the perimeter of this hexagon would be 11 * 7, as it is implied that it is a regular polygon ⇒ Perimeter: 77 units

2. Now let us substitute the apothem and perimeter into this formula to determine the area of this regular polygon: 1/2 * 11.5 * 77 ⇒ 442.75

Area of regular polygon: ( About ) 442.8 units^2

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

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