Edge of prism

The regular quadrilateral prism has a surface of 250 dm², its shell has a content of 200 dm². Calculate its leading edge.

Correct answer:

a =  5 dm

Step-by-step explanation:

$$\begin{gathered} S_1=250{\text{dm}}^2 \\ {S}_2=200{\text{dm}}^2 \\ {S}_1=2\cdot a^2+S_2 \\ a=\sqrt{(S_1-S_2)\mathrm{/}2}=\sqrt{(250-200)\mathrm{/}2}=5\text{ dm} \end{gathered}$$

Try another example

Related math problems and questions:

• Quadrilateral pyramid
  In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the diagonal of the base is 50 cm. Calculate the pyramid shell area.
• 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
• A regular
  A regular triangular prism with a base edge of 20 dm and a height of 30 dm is drawn. Find the volume of the prism and the area of the shell.
• Quadrilateral prism
  Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m², length of the base edge a = 14 dm, height of the prism 1,500 mm.
• Quadrilateral prism
  The surface of the regular quadrilateral prism is 8800 cm², the base edge is 20 cm long. Calculate the volume of the prism
• Tereza
  The cube has an area of base 256 mm². Calculate the edge length, volume, and area of its surface.
• The cube
  The cube has a surface area of 216 dm². Calculate: a) the content of one wall, b) edge length, c) cube volume.
• Quadrilateral prism
  Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
• 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?
• Regular square prism
  The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
• Regular prism
  The regular four-sided prism has a base of 25 cm² and a surface of 210 cm². Find its volume.
• 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?
• Quadrilateral pyramid
  A regular quadrilateral pyramid has a volume of 24 dm³ and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
• Calculate
  Calculate the surface of a regular quadrilateral prism whose base edge is 2.4dm and the height of the prism is 38cm.
• 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?
• Prism
  Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
• The regular
  The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.