A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.

# Tag: trapezium

## The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

## The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

## Parallelism

A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?

## Pulling the strings

Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.

## The wall between us

Two circles inscribed an a trapezium divided by a perpendicular line segment. What is the proportion of its length a and the side b?

## The green trap

A circle with its centre in the origin is cut by two parallel lines that are a distance d apart. One line is passing through the leftmost and one through the lowest point of the circle. What is the area of the green trapezium in terms of d?

## The leaning tower

A trapezium with it’s diagonals. Two areas are given. What faction is coloured?

## The three rights

A trapezium containing three right angles is split in two. What is the proportion of the areas yellow : blue?

## The paper hat

A rectangle and several triangles. The orange triangle has the same area as the green trapezium. What’s the total coloured fraction?