The roof

The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste.

Correct answer:

x =  255.4903 m²

Step-by-step explanation:

$$\begin{gathered} a=11\text{ m } \\ \alpha =57\mathrm{°}\to \text{ rad}=57\mathrm{°}\cdot {\displaystyle \frac{\pi }{180}}=57\mathrm{°}\cdot {\displaystyle \frac{3.1415926}{180}}=0.99484=19\pi \mathrm{/}60 \\ q=15\mathrm{\%}=1+{\displaystyle \frac{15}{100}}=1.15 \\ \cos \alpha =a\mathrm{/}2:h_1 \\ {h}_1=a\mathrm{/}2\mathrm{/}\cos (\alpha )=11\mathrm{/}2\mathrm{/}\cos (0.9948)\doteq 10.0984\text{ m } \\ {S}_1={\displaystyle \frac{a\cdot h_1}{2}}={\displaystyle \frac{11\cdot 10.0984}{2}}\doteq 55.5414{\text{m}}^2 \\ x=4\cdot S_1\cdot q=4\cdot 55.5414\cdot 1.15=255.4903{\text{m}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• House roof
  The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m² is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
• Regular quadrangular pyramid
  How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
• Tower
  The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m² of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
• Pyramid 8
  Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
• Base diagonal
  In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
• The bus stop
  The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how much m² roofing is required to cover the sheathing three walls, taking 40% of the additional coverage.
• Roof cover
  Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
• Roof 7
  The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m² of plate?
• Cone
  Calculate volume and surface area of ​​the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°.
• Roof 8
  How many liters of air are under the roof of the tower, which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
• Pyramid roof
  2/4 of the area of ​​the roof-shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?
• Top of the tower
  The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• The tent
  The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?
• The roof
  The roof has a spherical canopy with a base diameter of 8 m and a height of 2 m. Calculate the foil area with which the roof is covered when calculating 13% for waste and residues.
• Pyramid - angle
  Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.
• Church roof 2
  The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m² of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
• Hexagonal pyramid
  Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.