The picture shows a rectangle divided into two parts.
Instead of the broken line separating these parts, draw a straight line to divide the rectangle into two other parts of the same area. Calculate the areas ofthese parts.

The pictures below show circles through the vertices of a square and a rectangle.Calculate the areas of the circles

The picture below shows a trapezium divided into four parts by the diagonals. The area of the blue triangle is 4 square centimetres and area of the green triangle is square centimeters. What is the total area of the trapezium ?

In the picture below, the top vertex of a triangle is joined to the midpoint of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices. Prove that the areas of all three triangles in the picture on the right are equal to a third of the area of the whole triangle

In the picture below, the top vertex of a triangle is joined to the midpont of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices: Prove that the areas of all three triangles in the picture on the are equal to a third of the area of the whole triangle.

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length. Calculate the perpendicular sides of the large triangle.

The area between x=y^2 and x=4 is divided into two equal parts by the line x=a, find the value of a.

The picture on the right shows two circles centred on the same point and a line intersecting them.Prove that the parts of the line between the circles on either side are equal.

The picutre on the right shows two circles centred on the same point and the line intersecting them.Prove that the parts of the line between the circles on either side are equal.

The picture shows an equilateral triangle cut into halves by a line through a vertex. What is the perimeter of a part? .

The picture below shows two circles, each passing through the center of the other. Calculate the area of the region common to both.