Find the area of the heptagon formed by joining the points A(1,4), B(0,-3), C(2,3),   D(-1,2), E(-2,-1), and F(3,0) G(2,2).

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: 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: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 3,…

A: Consider the provided question, Let the vertices of the parallelepiped are A, B, C and D.

Q: What is the area of the triangle formed if it bounded by the x and y axes and the line,  2x - 3y =9?

A: Here we have to find the area of the traingle since Area of  Triangle = 1/2 *(hight)*base

Q: 10.7 -> 122 11.3 11.3 22.7

A: This question is based on Area of trapezoid formula.

Q: Find the area of the triangle with vertices P=(1,1,0), Q=(0,2,1) and R=(2,0,0).

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Q: The new owner of an apartment wants to install a window in the shape of a rectangle surrounded by a…

A: The total amount of wood owner has is equal to the perimeter thus add the add the two sides of the…

Q: Show that of all rectangles with diagonal of length c, the square has the largest area.

A: using second derivative test to find if square has largest area.

Q: snip

A: Given Parallelogram vertex।  A(1,1,1,1)  B(2,3,4) C(6,5,2) , D(7,7,5) Area = ∥AB ×AD∥ AB =…

Q: 2. Find the area of the triangle with vertices (0,0), (3,1) and (1,2)

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Q: 28, g6) = 2x2 [,3],8 reclanyles

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Q: Find the volume of the parallelepiped determined by the vertices A(1,1,1), B(4,7,2), C(3,2,1) and…

A: Let the vertex A(1,1,1) be taken as the point from which all measurements are taken. Calculate AB→,…

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: The area of parallelogram whose adjacent sides are i^-2j^+3k^ and 2i^+j^-4k^ is

A: Given sides arei^-2j^+3k^  &  2i^+j^-4k^

Q: J (1,4) M(-1, 2) К(3,2) L (1, – 3)

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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: The area of the parallelogram with two adjacent sides that are formed by V = i+j-2k and w= 2i-j-k is

A: Given,          The two adjacent sides vectors are v→=i+j-2k and w→=2i-j-k.We know that,…

Q: Find the area of the triangle determined by the points P(-3, 6, -4), Q(8, 8, -5), and R(-1, -1, -7).

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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: Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(1, 2, 0), C(0,…

A: Draw the diagram roughly

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: Find the area of the parallelogram. P1 (1, 2, 0), P2 (-3, 3, 4), P3 (0, -3, 3)

A: Given points are, P11,2,0P2-3,3,4P30,-3,3

Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î +2j-7k…

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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: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: 2. Show that of all rectangles with diagonal of length c, the square has the largest area.

A: All rectangles with diagonal of length c, the square has the largest area.

Q: Find the area of the triangle with vertices (0,0,0), (4,-4,1), and (4,-3,0)

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Q: What is the area of the parellelogram ABCD if the coordinates of the vertices are A (5,0), B (8,2),…

A: Explanation and solutions is given below....

Q: Find the area of the rectangle ABCD with vertices 4(-3,0), B(3,2), (4,-1), and D(-2,-3) B(3,2) 2…

A: Area of rectangle is length× Breadth

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 volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0,…

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Q: If the interval [1, 9] is partitioned into 4 subintervals of equal length, what is ∆x? List the grid…

A: Since n = 4 on the interval 1, 9 then                                               ∆t=b-an=2 where…

Q: Find the area of the polygon PQRS with its vertices at P(1, – 1), Q(6, -1), R(6, -6), and S(1, -6).

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Q: Find the area of the triangle having vertices at P (1,3,2), Q (-2,1,3) and R (3,-2,-1)

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Q: what is the area of ABC with vertices a (4, 1), b (2,-1), and c (-2, -1)?

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Q: Find the area of the parallelogram with adjacent sides u = (4, 3, 0) and v = (0, 3, 1).

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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: Let Q be the quadrilateral with vertices (-2,3), (1,4), (3,0), and (-1,–3). Find the area of Q

A: Consider a quadrilateral Q with vertices  A−2,3,B1,4,C3,0 and D−1,−3

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 area of the largest rectangle that fits into the triangle with sides х — %3D1 ахis, у —…

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Q: Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1),…

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Q: Find the area of the triangle with vertices (1,0,0), (0, 2,0), and (0,0, 1).

A: Area of triangle when three points are given is half the modulus of the cross product of the two…

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

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Q: Find the area of the traingle formed by the points (8,-5),(-2,-7) and (5,1) byusing Herones formulla

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Q: Find the area of the parallelogram with vertices (0,0), (4,0), (5,2) and (1,2). (1,2) (5, 2) (0,0)…

A: Here, we need to find the area of the given parallelogram.

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

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the area of a rectangular garden with vertices at A(3,4), B(3,-2) C(8,4) and D(8,-2).

A: Given:  Vertices of rectangular garden:    A(3,4), B(3,-2) C(8,4) and D(8,-2)

Q: Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 2) and  (-1, 1)

A: Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 2) and  (-1, 1)

Q: Find the area of the triangle with the given vertices. (Hint: 1lu x v|| A(0, 0, 0), B(1, 0, 3),…

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Q: Find the area of the square whose side is 6x+ 3. 36 x2 + 36 X + 3 O6x2 O6x+36 X+9 O 36 x2 + 36 X + 9…

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