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- ...all four of whose faces are isosceles triangles. Find the volume of this pyramid.6 KB (870 words) - 09:14, 19 June 2021
- ...ngle along the sides of its midpoint triangle. What is the volume of this pyramid?7 KB (1,094 words) - 12:39, 16 August 2020
- Next, we complete t he figure into a triangular prism, and find its volume, which is <math>\frac{6\sqrt{2}\cdot 12\sqrt{2}\ Now, we subtract off the two extra [[pyramid]]s that we included, whose combined volume is <math>2\cdot \left( \frac{6\s6 KB (971 words) - 14:35, 27 May 2024
- ...four of whose faces are [[isosceles triangle]]s. Find the volume of this pyramid. Our triangular pyramid has base <math>12\sqrt{3} - 13\sqrt{3} - 13\sqrt{3} \triangle</math>. The a7 KB (1,086 words) - 07:16, 29 July 2023
- ...ngle along the sides of its midpoint triangle. What is the volume of this pyramid? ...ulting pyramid. Call this point <math>V</math>. Clearly, the height of the pyramid is <math>z</math>. The desired volume is thus <math>\frac{102z}{3} = 34z</m7 KB (1,175 words) - 12:26, 3 September 2024
- ...ivided by 3) we have <math>\dfrac{rF}{3}=V</math>. The surface area of the pyramid is <math>\dfrac{6\cdot{4}+6\cdot{2}+4\cdot{2}}{2}+[ABC]=22+[ABC]</math>. We Next, we find the total surface area as the sum of the areas of the four triangular faces:8 KB (1,241 words) - 12:47, 1 October 2024
- ...dii to <math>A</math>,<math>B</math>, and <math>C</math> form a triangular pyramid <math>OABC</math>. We know the lengths of the edges <math>OA = OB = OC = 204 KB (614 words) - 17:12, 17 November 2024
- ...p, right, left, and bottom. Knowing that each quarter of each figure has a pyramid structure, we know that for each quarter there are <math>\sum_{n=1}^{100} n ...n <math>a_n</math>, the number multiplied by the 4 is the <math>n</math>th triangular number. Hence, <math>a_{100}=4\cdot \frac{100\cdot 101}{2}+1=\boxed{\textb8 KB (1,221 words) - 10:34, 27 November 2024
- ...polyhedron]]. Tetrahedra have four [[vertex|vertices]], four [[triangle | triangular]] [[face]]s and six [[edge]]s. Three faces and three edges meet at each ve1 KB (205 words) - 11:54, 20 February 2024
- ...olygonal base together with [[line segment]]s which join the vertex of the pyramid to each vertex of the polygon. The [[volume]] of a pyramid is given by the formula <math>\frac13bh</math>, where <math>b</math> is the2 KB (329 words) - 20:05, 20 August 2021
- ...ace]]s. The term is most frequently to refer to a polyhedron with eight [[triangular]] faces, with four meeting at each [[vertex]]. ...gular octahedron can be decomposed into two [[square (geometry)|square]] [[pyramid]]s by a plane constructed [[perpendicular]] to the space [[diagonal]] joini1 KB (157 words) - 17:48, 5 September 2024
- ...he [[vertex]]. The [[edge|edges]] of the tetrahedron are the sides of the triangular base together with [[line segment]]s which join the vertex of the tetrahedr1 KB (178 words) - 10:32, 29 March 2012
- A unit [[cube]] is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then ...se area <math>\frac{1}{4}</math>, so using the formula for the volume of a pyramid, <math>\frac{1}{3} \cdot \left(\frac{1}{4}\right) \cdot (1) = \frac {1}{12}2 KB (215 words) - 12:56, 19 January 2021
- Triangular numbers and Square numbers can be represented in the following manner: Find a pair of consecutive Triangular Numbers and the difference between a pair of consecutive Square Numbers wh11 KB (1,738 words) - 18:25, 10 March 2015
- ...6</cmath> because we can consider the tetrahedron to be a right triangular pyramid.2 KB (302 words) - 03:51, 16 January 2023
- A tetrahedron with four equilateral triangular faces has a sphere inscribed within it and a sphere circumscribed about it. ...tetrahedron <math>ABCD</math>, and let <math>O</math> be the center. Then pyramid <math>[OABC] + [OABD] + [OACD] + [OBCD] = [ABCD]</math>, where <math>[\ldot3 KB (522 words) - 10:39, 3 October 2023
- ...ther four faces of the pyramid. What is the edge-length of the base of the pyramid? ...ath> AB </math> respectively. Lastly, let the hemisphere be tangent to the triangular face <math> ABE </math> at <math> P </math>.2 KB (376 words) - 22:14, 5 January 2024
- ...yramid and its opposite face has all its edges on the lateral faces of the pyramid. What is the volume of this cube? We can use the Pythagorean Theorem to split one of the triangular faces into two 30-60-90 triangles with side lengths <math>\frac{1}{2}, 1</m3 KB (508 words) - 18:26, 7 August 2023
- ...n the set of points <math>(x,y,z)</math> is a tetrahedron, or a triangular pyramid. The point <math>(x,y,z)</math> distributes uniformly in this region. If th After cutting off a slice corresponding to <math>|x-y|< 1</math>, we get two triangular prisms, as shown in the figure.13 KB (2,131 words) - 16:24, 11 October 2024
- ...PCN].</math> But the volume of <math>DPCN</math> is simply the volume of a pyramid with base <math>1</math> and height <math>.5</math> which is <math>\frac{1} ...MBQ and DBCNQ. Then, we have the sum of the volumes of a tetrahedron and a pyramid with a trapezoidal base. Their volumes, respectively, are <math>\tfrac{1}{410 KB (1,592 words) - 12:35, 4 April 2024