Each side of triangle ABC is divided into three equal parts. Find the ratio of the are of hexagon `P Q R S T U` to the area of the triangle ABC.

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If AC = 1, then the length of the median of triangle ABC through the vertex A is equal to

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

The perimeter of a triangle ABC is six times the arithmetic mean of the sines of its angles. If the side a is 1 then find angle Adot

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

Three particles, each of mass m are situated at the vertices of an equilateral triangle ABC of side L as shown in the figure. Find the moment of inertia of the system about the line AX perpendicular to AB in the plane of ABC

The ratio of the areas of two triangles with equal height is 3 : 2 . The base of the larger triangle is 18 cm . Find the corresponding base of the smaller triangle.

PQ is a vertical tower having P as the foot. A,B,C are three points in the horizontal plane through P. The angles of elevation of Q from A,B,C are equal and each is equal to theta . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is del . Then prove that the height of the tower is (abc) tantheta/(4)dot

The sides of triangle ABC satisfy the relations a + b - c= 2 and 2ab -c^(2) =4 , then the square of the area of triangle is ______