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.

The product of the arithmetic mean of the lengths of the side of a triangle ABC and harmonic mean of the lengths of the altitudes of the triangle is equal to (Delta is area of triangle ABC).

In Fig. 9.29 ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD.

Three straight lines are drawn through the three vertices of a triangle ABC, the line through each vertex being parallel to the opposite side. The triangle DEF is bounded by these parallel lines. Consider the following statements in respect of the triangle DEF : 1. Each side of triangle DEF is double the side of triangle ABC to which it is parallel. 2. Area of triangle DEF is four times the area of triangle ABC. Which of the above statements is/are correct?

Pis a point inside the triangle ABC.Lines are drawn through P,parallel to the sides of the triangle.The three resulting triangles with the vertex at P have areas 4,9 and 49sq. units. The area of thetriangle ABC is -

Sides of triangle ABC, a, b, c are in G.P. If 'r' be the common ratio of this G.P. , then

In a triangle ABC with the right angle C, side BC is divided by points D and E into three equal parts.Find the sum of angles AEC,ADC, and ABC if it is known that BC=3AC

Find the ratio of the areas of an equilateral triangle ABC and square EFGC, if G is the centroid of the triangle ABC.