Question

Find the area of the regular polygon. Round your answer to the nearest tenth.

Answer 1

43.3

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 =
`\sqrt{10^(2) - (10/2)^(2) } = √(75) \\`

area of triangle = 1/2 x 10 x
`√(75)` = 43.30

Answer 2

43.30 km^2

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