A regular tetrahedron is a regular triangular pyramid in which all faces (lateral faces and base) are congruent. If each edge has length e, a) show that the area of each face is A = b) show that the total area of the tetrahedron is T = eV3. c) find the total area if each side measures e = 4 in.

Q: Find the volume of a square pyramid with base edges 9 and height 5.

A: Given Square pyramid with base edge 9 and height 5

Q: 4. Find the volume of a three-sided pyramid with height h and base an equilateral triangle with side…

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Q: For the right triangular prism found in Exercise 16, suppose that the sides of the triangular base…

A: Given that : For the right triangular prism, the sides of the triangular bases measures 3 ft , 4 ft…

Q: Find the volume of a regular square pyramid shown if each edge of the base measures 8ft. and the…

A: Volume = 1/3 * B * H B= area of the Base H= height ( altitude ) of the pyramid Given : b= 8 ft and…

Q: Suppose that each of the bases of the hexagonal prism in Exercise 1 has an area of 12 cm? and that…

A: The surface area of the solid is A=AL+2AB where AL is the total lateral surface area and AB is the…

Q: In the regular pentagonal pyramid, each base edge measures 9.2 cm and the apothem of the base…

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Q: Let ABCD be a rectangle, and let DM be a segment perpendicular to the plane of ABCD Suppose that DM…

A: Consider the given:

Q: A prism with height 2 m and a pyramid with height 5 m have congruenttriangular bases. Find the ratio…

A: Volume of Prism = area of base of prism × height   i.e. ,                     = A×2       (Let A…

Q: 11. The apothem and the height of a regular four-cornered pyramid are 8 cm and 4 cm respectively.…

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Q: Which set of dimensions belongs to a right rectangular prism with a volume of 440 cm3?

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Q: A regular hexagonal pyramid has a base whose sides are of length 6 V3 in. each. If the slant height…

A: Sketch the regular hexagonal pyramid as shown the below.

Q: For a regular square pyramid, the slant height of each lateral face has a measure equal to that of…

A:

Q: A hexagonal pyramid (not regular) with base ABCDEF has plane symmetry with respect to a plane…

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Q: In the accompanying regular pentagonal prism, suppose that each base edge measures 9 in. and that…

A: Given,  Length of base edge (b) = 9 in Altitude of prism (h) = 10 in Apothem of the base = 6.2 in

Q: Find the volume of a pyramid whose base is a square with side L and whose height is H

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Q: Find the total surface area of a frustum of a right square pyramid whose upper and lower base edges…

A: To find out the total surface area of a frustum of a right square pyramid.

Q: For a regular square pyramid with height 4 in. and base edges of length 6 in. each, find the length…

A: From the figure shown above - b = base length = 6 inchesh = height = 4 inchess = l = slant height =…

Q: Find the volume of a sphere pyramid of height "h" and base edge of length "a"

A:

Q: A regular pentagon has an apothem of length 4.0 in. and each side is of length 5.8 in. For the…

A: Given

Q: The Moscow Papyrus gives a formula for the volume of a truncated square pyramid as (a² + ab + b³) V…

A:

Q: ind the volume of the tetrahedron having the given vertices. (-6, –6, –5), (5, 4, –4), (4, –6, –3),…

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Q: In the regular pentagonal pyramid, each lateral edge measures 8 in., and each base edge measures 6…

A: Area of a pentagon is: Area=52×Apothem×Base side Area of a triangle using Heron's formula:…

Q: Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 cm? and that…

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Q: A regular tetrahedron is a regular triangular pyramid in which all faces (lateral faces and base)…

A: Given that, A regular tetrahedron is a regular triangular pyramid in which all faces (lateral faces…

Q: Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 in and that…

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Q: Suppose that each of the bases of the hexagonal prism in Exercise 1 has an area of 12 cm² and that…

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Q: A regular icosahedron has a volume of 200cm3. Find the length of the edge.

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Q: Find the volume of a regular icosahedron with edge equal to 10 cm. Select one: O a. 2,240 cm3 O b.…

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Q: Find the volume of the described solid SA tetrahedron with three mutually perpendicular faces…

A: Consider the x-y plane: Equation of a line passes through (0, 23) and (25, 0) is, y-y1=mx-x1…

Q: What is the volume of a regular hexagonal pyramid with base side length of 6 cm, apothem of 5.2 cm,…

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Q: It is possible for a right hexagonal prism with a volume of 840 cubic feet to have which of these…

A:

Q: Let V be the volume of a pyramid of height 15 whose base is a square of side 5. 5

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Q: It is possible for a right hexagonal prism with a volume of 840 cubic feet to have which of these…

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Q: A regular hexagonal pyramid has a slant height of 4 cm and the length of each side of the base is 6…

A:

Q: The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and…

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Q: What is the best approximation of the volume, in cubic units, of a pyramid of height 4 and a square…

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Q: 10. Compute the volume and surface area of a right regular octagonal pyramid for which the side of…

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Q: In the accompanying regular pentagonal prism, suppose that each base edge measures 6 in. and that…

A: a) Obtain the lateral area of the given prism as follows. Lateral Area,…

Q: A square based prism and a cylinder both have the same height of 4cm^3, based on the concepts of the…

A:

Q: The edge of a regular dodecahedron is 6 m, what is its total surface area?

A: Given:  The edge of a regular dodecahedron is 6 m. To Find: Total surface area of the given regular…

Q: Find the lateral surface area of a frustum of a right square pyramid if the upper and lower base…

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Q: A triangular pyramid has four congruent faces. The triangular face measures 11 inches high and 8…

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Q: For a right circular cone, the slant height has a measure equal to twice that of the radius length…

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A: Consider the given figure as

Q: Find the volume of a frustum of a regular pyramid with hexagonal bases whose sides are 4cm and 6cm,…

A: To find the volume of a frustum of a regular pyramid with hexagonal bases whose sides are 4 cm and 6…

Q: Given four trapezoids of width 1, calculate the area of the shaded region.

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Q: For the regular square pyramid shown, suppose that the sides of the square base measure 10 m each…

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