Resources by Something in Common

Trapezium and Diagonals

The opposite corners of a trapezium are joined, creating four triangles within the trapezium. The areas of the triangles formed using the parallel sides as is given. The task is to calculate the...

Triangle multiple

A triangle is split into two parts by drawing a line from one side to the base of the triangle. The ratio in which the sides are split is shown for each of the sides connected by the line. The task is to find what multiple of the smaller triangle is the larger triangle.

The ‘something in common’ between each...

Triangle tan product and sum

In this resource the side lengths of a triangle are given. The challenge is to find the ratio of the product of each of the tangents, divided by the sum of each of the tangents.

Each student worksheet contains a different triangle, but the answers all have something in common.

The solution involves...

Triangle xy Area

A circle is drawn that is tangent to the three sides of the triangle. The two constituent lengths of the hypotenuse are given and the challenge is to calculate the area of the triangle. When...

Two crescents and a triangle

This resource contains a diagram made from a circle, four semi-circular arcs and a rectangle with dimensions given in surd form. The challenge is to find the total area of a given shaded area.

The student worksheets each contain different dimensions for the diagram, but the solutions all have something in...

Volume of a Tetrahedron

The coordinates of the vertices of a tetrahedron is given. The challenge is to work out the volume of the tetrahedron. This involves calculating the area of the base,...

Wedged triangles

In this resource students are given an image of a reciprocal curve, y=k/x. Two tangents to the curve are used, together with the coordinate axes, to form an 'arrow head' quadrilateral under the curve. The challenge is to determine the area of the quadrilateral.

The first step towards solving the problem...

What’s f(500)?

A function is defined so that f(xy) = f(x) + f(y) for all positive integers x and y. Students are given the value of f(10) and (40) and are challenged to determine the value of f(500).

In each student worksheet contains different values for f(10) and f(40) but for...

What’s the Sine Rule Ratio?

A triangle is shown divided into two regions by a straight line, resulting in the triangle being split into a smaller triangle and a cyclic quadrilateral. A task is set to determine the ratio of an angle and an opposite side. In each of the numerical examples given the answer to 6 significant figures is 14.

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