Answer:
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a. 350 unit²
b. 81.23 unit²
c. 41.57 unit²
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Beth should buy 3 bags of fertilizer
Step-by-step explanation:
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a. The figure consists of 9 isosceles triangles of side lengths 11 and vertex angle = 360/9 = 40°
Hence base angles = (180 - 40)/2 = 70°
Therefore, the base of the triangles = sin(40) × 11/sin(70) = 7.52
Hence area of figure = 9 × 0.5 × 7.52 × √(11² - (7.52/2)²) =349.99 ≈ 350 unit²
b. Area of a decagon
We note that the vertex angle = 36°
∴ Half the base = tan(18) × 5 = 1.62
Area = 10 × 1.62 × 5 = 81.23 unit²
c. The area of a hexagon = [tex]s^2 \times \dfrac{3\sqrt{3} }{2}[/tex]
s = 4 therefore, the area = [tex]4^2 \times \dfrac{3\sqrt{3} }{2} = 41.57 \, unit^2[/tex]
8 - 36
Area, A of a regular pentagon = [tex]A = a^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex]
a = 15 ft., therefore, A = [tex]15^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex] = 387.11 ft.²
Therefore, since a bag of fertilizer can fertilize 150 ft.², the number of bags of fertilizer that will fertilize 387.11 ft.² will be 387.11/150 = 2.58 bags
Therefore, since 2 bags of fertilizers will not be enough, Beth should buy 3 bags of fertilizer.
