Triangle + pyramid - practice problems
Number of problems found: 183
- Januka
Januka and her father were going to the tent. They found that their old tent was torn. Their mother suggested that they sew a tent whose walls would be made of 4 identical isosceles triangles. Their lower side is 2 m long, and the height is also 2 m. Then - Storage shed
Frank designed a net for a storage shed that he is going to construct out of metal. The design consists of a square base and four square sides, plus four triangular parts that make up the roof. A square base of 6 feet and four square sides, plus 4 feet of - Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8 - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
- 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. - Church roof
The roof of the church tower has the shape of a regular tetrahedral pyramid with a base edge length of 5.4 meters and a height of 5 m. It was found that the 27% covering of the roof area needs to be corrected. What amount of material will be required? - CoG center
Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all case - 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. - Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is its area (surface area)?
- Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Hexagonal pyramid
Find the area of a shell of the regular hexagonal pyramid if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. - 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. - Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - Slant height 2
A regular triangular pyramid with a slant height of 9 m has a volume of 50 m³. Find the lateral area of the pyramid.
- Calculate 26991
How can you calculate the wall height of a pyramid when you know: the length of the base edge: is 28 mm and: the body height: is 42 mm? - Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the pyramid's height is 7 cm. - Pyramid
Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate the angle between plane ABV and the base plane b) calculate the angle between opposite side edges. - Lamp cone
Calculate the surface of a lampshade shaped like a rotary truncated cone with a base diameter of 32 cm and 12 cm and a height of 24 cm. - Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm.
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