If ABC is an isosceles triangle with AB = AC. E and F are points on BC and AC respectively such that AE = AF. If ∠BAE = 40°, then ∠FEC is equal to

ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF?

X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?

ABC is a triangle in which AB = 3 cm, BC = 4 cm and ∠B = 90°. The circle with diameter AB intersects AC at D and tangent to the circle at D intersects BC at E. Then EC is equal to

If the area of a square is equal to the area of an equilateral triangle, the ratio of the side of the square and the side of the equilateral triangle is

The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse ?