What is the area of the regular polygon? It is a three sided polygon with the apothem of 7m?

That's an equilateral triangle (a three sided regular polygon) with a height of 7 m.

The equilateral triangle bisected along its altitude is the biggest cliche in geometry, the 30/60/90 right triangle, sides in ratio 1:√3:2.  

In this story the apthem is the height, let's call it h, and we'll call the other leg w.  w:h=1:√3 so w = h/√3

The area of the 30/60/90 triangle is wh/2 and the equilateral triangle is two of these so its area Δ is

Δ = wh = h²/√3

We have h = 7m

Δ  = 49/√3  ≈ 28.290163190291665

We could move the radical to the numerator for a high school ready exact answer but I'll just say

49/√3 square meters

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

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