ABCD is a square of side a. A line parallel to the diagonal BD at a distance x from the vertex A cuts the two adjacent sides. Express the area of the segment of the square with A at a vertex, as a function of x.

Find the area of a parallelogram. Also find the length of the altitude from vertex A on the side DC.

If (a, b) be an end of a diagonal of a square and the other diagonal has the equation x-y=a , then another vertex of the square can be

One side of a square is inclined to the x-axis at an angle alpha and one of its extremities is at the origin. If the side of the square is 4, find the equations of the diagonals of the square.

x and y are the sides of two squares such that y=x-x^2 . Find the rate of the change of the area of the second square with respect to the first square.

Sum of the areas of two squares is 468 m^2 . If the difference of their perimeters is 24 m, find the sides of the two squares.

A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is y(sqrt(3)-1)-x(1-sqrt(3))=2a y(sqrt(3)+1) +x(1-sqrt(3))=2a y(sqrt(3)+1)+x(1+sqrt(3)) =2a y(sqrt(3)+1)+x(sqrt(3)-1)=2a

If two adjacent sides of the parallelogram are (3x+5y) and (2y-x) then find its perimeter.

The area of the square ABCD is 64 sq. cm. Find the area of the square joining the mid points of the sides of square ABCD.

Prove that any line segment drawn from the vertex of a trianlge to the base is bisected by the line segment joining the mid points of the other sides of the triangle.

The side of a square exceeds the side of another square by 4 cm and sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares.