Find the area of the regular polygon. Round your answer to the nearest tenth.
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Answer:
43.30 km^2
Step-by-step explanation:
Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula
Working:
Side is 10
Perimeter= 30km
Semiperimeter (s) = 15km
Formula= √s(s-a)(s-b)(s-c)
= √15(15-10)(15-10)(15-10)
= √15*5*5*5
=5√5*15
=5√75
= 5*8.66
= 43.3 km^2
Answer:
43.3
Step-by-step explanation:
since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60
use formula 1/2 x a x b x sin C where a and b are sides and C is the angle
1/2 x 10 x 10 x sin 60 = 43.30
or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km
h = [tex]\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\[/tex]
area of triangle = 1/2 x 10 x [tex]\sqrt{75}[/tex] = 43.30