The Scout Tent

The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high pyramid roof?

Correct answer:

x =  7.1251 m²

Step-by-step explanation:

$$\begin{gathered} a=220\text{ cm}\to \text{ m}=220\mathrm{/}100\text{ m}=2.2\text{ m } \\ b=150\text{ cm}\to \text{ m}=150\mathrm{/}100\text{ m}=1.5\text{ m } \\ h=170\text{ cm}\to \text{ m}=170\mathrm{/}100\text{ m}=1.7\text{ m } \\ {h}_1=\sqrt{h^2+(b\mathrm{/}2{)}^2}=\sqrt{1.7^2+(1.5\mathrm{/}2{)}^2}\doteq 1.8581\text{ m } \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{1.7^2+(2.2\mathrm{/}2{)}^2}\doteq 2.0248\text{ m } \\ {S}_1=a\cdot h_1\mathrm{/}2=2.2\cdot 1.8581\mathrm{/}2\doteq 2.0439{\text{m}}^2 \\ {S}_2=b\cdot h_2\mathrm{/}2=1.5\cdot 2.0248\mathrm{/}2\doteq 1.5186{\text{m}}^2 \\ x=2\cdot (S_1+S_2)=2\cdot (2.0439+1.5186)=7.1251{\text{m}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Insulate house
  The property owner wants to insulate his house. The house has these dimensions 12, and 12 m is 15 m high. The windows have 6 with dimensions 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need?
• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
• Cube and sphere
  Cube with the surface area 150 cm² is described sphere. What is sphere surface?
• The quadrilateral pyramid
  The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
• Tablecloths
  The restaurant has sixty-two square tablecloths with a side length of 150 cm and 36 rectangular tablecloths with dimensions of 140 cm and 160 cm. A) How many meters of hemming ribbon will be needed if we add 50 cm to each tablecloth? B) The ribbon sale in
• Quadrilateral pyramid
  Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
• Two sides paint
  The door has the shape of a rectangle with dimensions of 260cm and 170cm. How many cans of paint will be needed to paint this door if one can of paint cover 2m² of the area? We paint the doors on both sides.
• Cuboid - volume and areas
  The cuboid has a volume of 250 cm³, a surface of 250 cm² and one side 5 cm long. How do I calculate the remaining sides?
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Isosceles trapezoid
  The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
• The tent
  Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
• The pool
  The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
• Sails
  We known heights 220, 165, and 132 of sail. It has a triangular shape. What is the surface of the sail?
• Pyramid
  The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
• Rotating cone
  Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm.