A cube of edge 4 in is cut by a plane containing two diagonally opposite edges of the cube. Find the area of the section formed.

Q: Find the angle between a diagonal of a cube and an ad­jacent edge.

A: Let the side of the cube is of length s. Let us take the side of thr cube to be vector<s,0,0>…

Q: Exercise 1. Find the area of the polygon in R³ with corners (3, –4) (-7, 7), (5, 5), (–5, –6) and

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(2, 0, –1), Q(4, 1, 0),…

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Q: The prism is bisected by the xz-plane. If P = (5, 2, 4), what is the area of the rectangle formed by…

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Q: cube of edge 4 is in cut by a plane containing two teo diagonally opposite edges of the cube. Find…

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Q: A right pyramid 10m high has a square base of which the diagonal is 10m. Find the area of the…

A: Geometrical  pyramid  Area is   150 square meter

Q: 24. Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,…

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Q: Prove (via geometry) that the area of a cyclic quadrilateral is the maximum possible for any…

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Q: Find the volume of the parallelepiped with adjacent edges  PQ, PR,  and PS. P(−2, 1, 0), Q(5, 2,…

A: Given : The four points are given as, P-2,1,0, Q5,2,5 , R1,4,-1  and S3,6,1 To  find: The volume of…

Q: Find the area of an isosceles trapezoid with legs 7 and bases 11 and 21.

A: Consider the  isosceles trapezoid ABCD.

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: The base of the rectangular pyramid shown above has one side that measures 5 inches, one side that…

A: To determine the area of the vertical cross-section of the pyramid that is parallel to longer side…

Q: Find the total area (surface area) of a regular tetrahedron if each edge has a length of 6 in.

A: Length of an edge of a regular tetrahedron is 6 inches.

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right…

A: Given: AF=4, AD=5, and DF=3. AC= (4-h) and DE= (3-w) Therefore,

Q: The radius of the largest sphere with center (29,330,290) that is contained in the first octant is…

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Q: Sketch the triangle with vertices at the origin O, P = (3, 3, 0), and Q = (0, 3, 3), and compute its…

A: The area of the triangle using the cross products is defines as Area=12v×u Here, v is the vector…

Q: Each side of square RSTV has length 8. Point W lies on VR and point Y lies on TS in such a way to…

A: Area of the square RSTV is, Area of square RSTV=Area of triangle RSW+Area of Parallelogram VWSY+Area…

Q: 5. Find the length of the shorter diagonal in a rhombus with an area of 30 m² if the lengths of the…

A: Given: Area =30m2 length of diagonal differ by 4

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

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Q: Find the smallest possible area of an isosceles triangle thatis circumscribed about a circle of…

A: To Find: The Smallest Possible area of an isosceles triangle that is circumscribed about a circle of…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(5, 3, 5),…

A: Given three vectors, there is a product, called scalar triple product, that gives (the absolute…

Q: J (1,4) M(-1, 2) К(3,2) L (1, – 3)

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS: P(-2,1,0), Q(2,3,2),…

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Q: K.

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Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0,…

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS…

Q: How many planes are shown in the figure? *

A: Given geometry is hexagon prism. Hexagon is a regular polygon made up of six edges. When the edges…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(-2,1,0), Q(2,3,2),…

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Q: Suppose that a circle of radius r is inscribed in a rhombus, each of whose sides has length s. Find…

A: Find an expression for the area of the rhombus in terms of r and s.

Q: What is the maximum area of a rectangle inscribed in a right triangle with legs of length 3 and 4 as…

A: Given: Formula used: The area of a rectangle is length * width.

Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r

A: Let the length of the rectangle be 2x and the width of the rectangle be y. From the figure, the…

Q: All nine edges of a right triangular prism are congruent. Find the length of these edges if the…

A: Solution: Consider the given right triangular prism. Also, it is given that the volume is 543 cm3 We…

Q: Show that the volume of a parallelepiped with sides A, B and C is given by A · (B × C)

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Q: Find the volume of the parallelepiped with. adjacent edges PQ, PR, and PS, where P(-2,1,0),…

A: Given- P-2,1,0,Q2,3,2,R1,4,4 and S3,6,1 To Find- The volume of the parallelepiped with the adjacent…

Q: Calculate the area of the given quadrilateral starting at A and going clockwise using the shoelace…

A: Topic = Area

Q: Find the volume of the parallelepiped with adjacent edges PQ, where P (1,1, 1), Q (2,0,3,), R =…

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Q: Find the volumes of thetetrahedra whose vertices are A(0, 0, 0), B(2, 0, 0), C(0, 3, 0), D(0, 0, 4)

A: Consider the following vertices: A0,0,0, B2,0,0, C0,3,0, D0,0,4…

Q: Show that among regular polygons having the same perimeter, the area increases with the number of…

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Q: Prove that among all rectangles with area 100 square units,the square has the smallest perimeter.

A: The area of the rectangle is defined as the product of length and breadth of the rectangle, whereas…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(3, 4, 3),…

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Q: Find the volume of the parallelopiped with adjecent edges PQ, PR, PS where P(5,-2,-3), Q(7,1,0),…

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Q: Prove that of all triangles having two given sides of lengths a and b, the one whose sides form a…

A: It is given that the length of two sides of a triangle is a and b, respectively. It is known that…

Q: Prove that the area of a square whose diagonal has length d is A = ¿d?.

A: The length of the diagonal of a square is d. Now let a be the length of the side of a square. Now…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(3, 0, 1), Q(2, 3,…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2,…

A: The given points P-2,-1,-3, Q0,2,0, R-3,-2,-4, S4,-3,-1

Q: Find the volumes of thetetrahedra whose vertices are A(0, 0, 0), B(1, 0, 2), C(0, 2, 1), D(3, 4, 0)

A: The vertices of the tetrahedra are A(0, 0, 0), B(1, 0, 2), C(0, 2, 1), D(3, 4, 0). The volume of the…

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: Two cubes whose edges measure 3 cm, 4 cm and 5 cm respectively to form a single cube.Find its…

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Q: Find the area of a square whose diagonal has length V10 in.

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR and PS given the  points P = (−2,…

A: We have to find

Q: Determine the dimensions of the largest rectangle that could be inscribed in a semi-circle of radius…

A: