Finding the Volume of a Tetrahedron In Exercises 41-46, find the volume of the tetrahedron with the given vertices.
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Elementary Linear Algebra (MindTap Course List)
- Verifying a Polygon In Exercises 25-28, show that the points form the vertices of the polygon. Isosceles triangle: 1,3,3,2,2,4.arrow_forwardFind the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(3,1,0), C(0,-5,1), and D(5,-4,8). The volume of the parallelepiped with the given vertices A, B, C D is _____units cubed. (Simplify your answer.)arrow_forwardTrigonometry Find the perimeter and area of a polygon whose vertices are at (1, -4), (4, -1), (4,5), (-1,4), and (-2, -1)arrow_forward
- Area of a ParallelogramFind the areas of the parallelograms whose vertices are given in Exercises 35–40.arrow_forwardFind the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(3,1,0), C(0, -2,1), and D(2, -6,8). The volume of the parallelepiped with the given vertices A, B, C and D is (Simplify your answer.) units cubed.arrow_forward2(a) The shaded face of the cuboid is a square. Find the length of one side 2 points of the square face. * (a) Volume = 6000 cm 15 cm cmarrow_forward
- Find the area of the parallelogram with vertices P1, P2, P3 and P4- P = (1,2, - 1), P2 = (7,5, - 3), P3 = (3, – 3,2), P4 = (9,0,0) The area of the parallelogram is (Type an exact answer, using radicals as needed.) IIarrow_forward(b) A parallelogram has vertices at A(-3,0), B(-1,3), C (5,2) and D(3, –1). Find the area u- the parallelogram using the formula area = AB x AD|.arrow_forwardDetermine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (1, −2, −2), (3, −3, −4), and (−2, −2, 1). Volume = 0arrow_forward
- Rectangle ABCDABCD has vertices A(−9, 6)A(−9, 6), B(−3, 6)B(−3, 6), C(−3,−6)C(−3,−6), and D(−9,−6)D(−9,−6). It is dilated by a scale factor of 1313 centered at (0, 0)(0, 0) to produce rectangle A′B′C′D′A′B′C′D′. What is the perimeter in units of rectangle A′B′C′D′A′B′C′D′?arrow_forwardA "rotated" square is placed on a coordinate plane and two adjacent corners of the square are located at (-4,-3) and (1,-2) a what is the side length of the square b what is the areaarrow_forwardFind the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(1,3,0), C(0, – 4,3), and D(2, - 4,5). The volume of the parallelepiped with the given vertices A, B, C and D is units cubed. (Simplify your answer.)arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage