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Required shingle bundles = = 668.5 ≈ 669 bundles.

which costs 669 × 35.99 = 24077.31 dollars.

Step-by-step explanation:

Let us divide the roof into two parts 1) cuboid and 2) pyramid.

Now, lower part of the roof

1)  lateral surface of cuboid.

 each surface is a rectangle with length(l) 10.00 m and width(b) 2.32 m

 ⇒ area = l × b = 10 × 2.32 = 23.2 m²

 now, total area of lower part of roof = 4 × 23.2 = 92.8 m²

(4 rectangles / faces)

Now, upper part of the roof.

2) lateral surface of pyramid.

 given length of square base of pyramid (l) = 10.00 m

⇒ diagonal length (d) = 10√2 m.

 now, given total height of roof = 4.36 m

⇒ height of only upper part (pyramid), h = 4.36 - 2.32 = 2.04 m.

Now, one of the pyramid edges (a) , height of the pyramid (h) and half of the diagonal of the square base (d/2) makes a right angled triangle.

From pythagorus theorem,

(height of pyramid)² + (half-diagonal)² = (length of pyramid edge)²

⇒ h² + (d/2)² = a²

⇒ a² = (2.04)² + (50√2)² = 5004.1616

⇒ a = 70.7400 m.

Length of all the edges of pyramid are same in this case,

length of edge, a = 70.7400 m.

Now, consider one triangular face of pyramid with two of the sides being

a = 70.7400 m and 10.00 m

⇒ area of one face of pyramid =

where, p =

(area of triangle with sides a,b,c is )

Here p = .

p = 75.7400 m.

area of one face =

                             = 352.815 m²

Total area of upper part of roof = 4 × 352.815 = 1411.261 m²

Now, total area of roof = 92.8 m² + 1411.261 m² = 1504.061 m².

Given that one bundle of shingles cover 2.25 m²

Required shingle bundles = = 668.5 ≈ 669 bundles.

which costs 669 × 35.99 = 24077.31 dollars.

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step-by-step explanation:

9-15%

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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