Explain me how to get the answers forArea of triangleArea of PentagonArea of Hexagon Area of regular PolygonsTriangle: A = base x HeightSquare: A = s²; s = lenght of sideRegular Hexagon with Apothem: A =where; s = lenght of side2Apothem -the side.n = number of sides of a polygonsana = apothem- is the perpendicular distance from the center of the regular polygon to any ofT(n-2)2nFormula: a = tanNote: In degree mode = 180°apothem(radian mode) Area of PentagonSolution: Since the perimeter is 12, henceS = 12 + 5 = 2.4 inchesArea:apothem = tan ((2-2)2.4= 2/+tan (T(5-²))a =a = (1.2) tana = 1.6517 inchesa =a = (1) tan3TArea of HexagonSolution: Since the perimeter is 12, henceS = 12 + 6 = 2 inchesArea:apothem = tan ((n=2))= ²tan ((6-2))4πTa = tana = √3 inchesA = san ==P(a)2A = (2.4)(1.6517) (5)A = 9.9102 sq. inchesA =apothem= 1/sanA = ²(2)(√3)(6)A = 10.3923 sq. inchesapothem

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Answered: Triangle: A = base × Height Square: A =…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Explain me how to get the answers for Area of triangle Area of Pentagon Area of Hexagon

Area of regular Polygons
Triangle: A = base x Height
Square: A = s²; s = lenght of side
Regular Hexagon with Apothem: A =
where; s = lenght of side
2
Apothem -
the side.
n = number of sides of a polygon
san
a = apothem
- is the perpendicular distance from the center of the regular polygon to any of
T(n-2)
2n
Formula: a = tan
Note: In degree mode = 180°
apothem
(radian mode)

Area of Pentagon
Solution: Since the perimeter is 12, hence
S = 12 + 5 = 2.4 inches
Area:
apothem = tan ((2-2)
2.4
= 2/+tan (T(5-²))
a =
a = (1.2) tan
a = 1.6517 inches
a =
a = (1) tan
3T
Area of Hexagon
Solution: Since the perimeter is 12, hence
S = 12 + 6 = 2 inches
Area:
apothem = tan ((n=2))
= ²tan ((6-2))
4πT
a = tan
a = √3 inches
A = san =
=
P(a)
2
A = (2.4)(1.6517) (5)
A = 9.9102 sq. inches
A =
apothem
= 1/san
A = ²(2)(√3)(6)
A = 10.3923 sq. inches
apothem

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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