Plotted on the Cartesian plane its 4th vertex is at (1, 8) and it has sides of 2 Times Square root of 13 which gives it an area of 52 square units.
If you mean vertices at the points (-1, 5) and (-3, 1) then the area of the square works out as 20 square units
Select any one of the vertices and draw all the diagonals from that vertex. This will divide the polygon (with n sides) into n-2 triangles. Use the coordinates of the vertices of each triangle to calculate its area, and then add the areas of these triangles together.
A solid angle, measured from a vertex, is the ratio between the area subtended by the angle at the vertex and the the square of the distance to the vertex. The unit of measurement is the stradian.
The only thing that can be said is that the quadrilateral will have an area that is smaller than the square. The exact value depends on the location of the vertices.
I'm going to assume you mean that a square with area 100 units2 is inscribed in the circle.The area of the square is 100 units2, so the side of the square is 10 units long. The distance from the center of the square (also the center of the circle) to the midpoints of each side of the square is 5 units. Using the Pythagorean theorem, we find that the distance from the center to a vertex of the square is 5*sqrt(2) units.Since the vertices of the square lie on the circle, this is also the radius of the circle. The area of the circle is pi times the radius squared, or pi * 5*sqrt(2) * 5*sqrt(2) = 50*pi.
If you mean vertices at the points (-1, 5) and (-3, 1) then the area of the square works out as 20 square units
The shape described by those vertices is not a square.
It has a flat base, a curved surface area, a circular edge and one vertex.
Select any one of the vertices and draw all the diagonals from that vertex. This will divide the polygon (with n sides) into n-2 triangles. Use the coordinates of the vertices of each triangle to calculate its area, and then add the areas of these triangles together.
A solid angle, measured from a vertex, is the ratio between the area subtended by the angle at the vertex and the the square of the distance to the vertex. The unit of measurement is the stradian.
Assuming that these are coordinates of the vertices, the area is 6 square units.
The only thing that can be said is that the quadrilateral will have an area that is smaller than the square. The exact value depends on the location of the vertices.
I'm going to assume you mean that a square with area 100 units2 is inscribed in the circle.The area of the square is 100 units2, so the side of the square is 10 units long. The distance from the center of the square (also the center of the circle) to the midpoints of each side of the square is 5 units. Using the Pythagorean theorem, we find that the distance from the center to a vertex of the square is 5*sqrt(2) units.Since the vertices of the square lie on the circle, this is also the radius of the circle. The area of the circle is pi times the radius squared, or pi * 5*sqrt(2) * 5*sqrt(2) = 50*pi.
With the available information all that can be said is that the area of the second square will be less than that of the first. The question cannot be answered in any meaningful way without further information. For example, do the vertices of the second square lie on the sides of the first? How far from the vertices of the first? What angle is the second square rotated through?
By plotting the given vertices and then joining them together on the Cartesian plane the shape of a isosceles triangle will be formed with an area of 78 square units.
If you mean vertices of: (7, 3) (12, 3) (12, 11) (7, 11) then the area works out as 5 times 8 = 40 square units
A regular hexagon, one that is both equiangular and equilateral, has an area of 3 times the square root of three times the square of the side length, all divided by 2. Once the side length has been discovered, the area can easily be calculated. However, hexagons with irregular bounds can have their area found, if their vertices are known by coordinate. Multiply each vertex's x coordinate by the y coordinate of the next vertex (looping back around to the first for the sixth), taking the sum of the six numbers found. Then multiply each vertex's y coordinate by the next's x coordinate, once again summing up these six numbers. Finally, subtract the larger of the two by the smaller, and divide this number by 2. This will provide the area in the units of the plot used to find the coordinates.