The area of parallelogram; triangle and quadrilateral in terms of cross product.

Which of the following statements are true (T) and which are false (F)? In a parallelogram, the diagonals are equal. In a parallelogram, the diagonals bisect each other. In a parallelogram, the diagonals intersect each other at right angles. In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. If all the angles of a quadrilateral are equal, it is a parallelogram. If three sides of a quadrilateral are equa, it is a parallelogram. If three angles of a quadrilateral are equal, it is a parallelogram. If all the sides of a quadrilateral are equal it is a parallelogram

Obtain an expression for the area of a triangle in terms of the cross product of two vectors representing the two sides of the triangle

The area of a parallelogram is equal to the product of a side of the parallelogram and the distance between any two sides.

Given the following statements : A:If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. B: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. Identify these as contrapositive or converse of each other.

In Fig. 9.35, find the area of parallelogram ABCD if the area of shaded triangle is 9 cm^2 .

Area OF Triangle || Quadrilateral || Centres OF Triangle

Finding the area of figure which is combinations of triangles and quadrilaterals

The base of a parallelogram is (2x + 3) units and the corresponding height is (2x – 3) units. Find the area of the parallelogram in terms of x . What will be the area of parallelogram of x = 30 units?

Statement -I: A diagonal divides a parallelogram into two triangles of equal areas.Statement-II: Area of parallelogram can also beobtained by the product of two adjacent sides.

If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram, so formed will be half of the area of the given quadrilateral (figure).