Question

I need help with 8-35 and 8-36

Answer 1

8 - 35

a. 350 unit²

b. 81.23 unit²

c. 41.57 unit²

8 - 36

Beth should buy 3 bags of fertilizer

Explanation:

8 - 35

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 =
`s^2 * (3√(3) )/(2)`

s = 4 therefore, the area =
`4^2 * (3√(3) )/(2) = 41.57 \, unit^2`

8 - 36

Area, A of a regular pentagon =
`A = a^2 * (1)/(4) \sqrt{5(5 + 2√(5) )}`

a = 15 ft., therefore, A =
`15^2 * (1)/(4) \sqrt{5(5 + 2√(5) )}` = 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.