The pyramid 4s

The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of length 13 dm. Calculate the surface area and volume of this pyramid.

Correct answer:

S =  222.8492 dm²
V =  192 dm³

Step-by-step explanation:

$$\begin{gathered} a=6\text{ dm } \\ b=8\text{ dm } \\ e=13\text{ dm } \\ d=\sqrt{a^2+b^2}=\sqrt{6^2+8^2}=10\text{ dm } \\ h=\sqrt{e^2-(d\mathrm{/}2{)}^2}=\sqrt{13^2-(10\mathrm{/}2{)}^2}=12\text{ dm } \\ {S}_1=a\cdot b=6\cdot 8=48{\text{dm}}^2 \\ {s}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{12^2+(6\mathrm{/}2{)}^2}=3\sqrt{17}\text{ dm}\doteq 12.3693\text{ dm } \\ {s}_3=\sqrt{h^2+(b\mathrm{/}2{)}^2}=\sqrt{12^2+(8\mathrm{/}2{)}^2}=4\sqrt{10}\text{ dm}\doteq 12.6491\text{ dm } \\ {S}_2={\displaystyle \frac{a\cdot s_3}{2}}={\displaystyle \frac{6\cdot 12.6491}{2}}=12\sqrt{10}{\text{dm}}^2\doteq 37.9473{\text{dm}}^2 \\ {S}_3={\displaystyle \frac{b\cdot s_2}{2}}={\displaystyle \frac{8\cdot 12.3693}{2}}=12\sqrt{17}{\text{dm}}^2\doteq 49.4773{\text{dm}}^2 \\ S=S_1+2\cdot S_2+2\cdot S_3=48+2\cdot 37.9473+2\cdot 49.4773=222.8492{\text{dm}}^2 \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 48\cdot 12=192{\text{dm}}^3$

Try another example

Related math problems and questions:

• 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.
• Hexagonal pyramid
  Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• 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.
• 9-gon pyramid
  Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• Quadrangular pyramid
  The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
• 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.
• 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
• 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.
• Tetrahedral pyramid
  A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
• Pyramid in cube
  In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid.
• 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
• Rectangular base pyramid
  Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.
• Pentagonal pyramid
  The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
• 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.
• 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°.
• 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.
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.