Plane Geometry

Find the number of sides of a regular polygon if each interior angle measures 108 degrees.

Find the area of the triangle whose sides are 25, 39 and 40.

The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

In triangle ABC, AB = 40 m, BC = 60 m and AC = 80 m. How far from A will the other end of the bisector of angle B be located along line AC?

A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 30 degrees in a distance of 300 m?

A chord is 36 cm long and its midpoint is 36 cm from the midpoint of the longer arc. Find the radius of the circle.

Find the area of the largest circle which can be cut from a square of edge 4 in.

The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units?

The areas of a regular pentagon and a regular hexagon are both equal to 12 sq. cm. What is the difference between their perimeters?

In a circle of diameter 26 cm, a chord 10 cm in length is drawn. How far is the chord from the center of the circle?

The length of the median drawn to the hypotenuse of a right triangle is 12 inches. Find the length of the hypotenuse.

The area of a right triangle is 50. One of its angles is 45°. Find the hypotenuse of the triangle.

Find the area of the largest circle which can be cut from a square of edge 4 in.

The area of a rhombus is 264 sq. cm. If one of the diagonals is 24 cm long, find the length of the other diagonal.

Find the sum of the interior angles of a regular hexagon.

Find the ratio of the sides of a triangle if its sides form an arithmetic progression and one of the angles is 90 degrees.

Find the radius of the circle inscribed in the triangle determined by the lines \(y = x + 4\), \(y = -x - 4\) and \(y = 7x - 2\).

The sides of a right triangle are in arithmetic progression whose common difference is 6 cm. Its area is