Categories
Intermediate

Pandora’s box II

Five squares and a diagonal. What fraction of the largest square is coloured?

Categories
Intermediate

The square sail

A quadrilateral and a parallelogram share two sides, and a vertex from each determine the orange square. The lengths BC, EF, AD are 4,5,7 respectively, where E and F are midpoints of AB and DC. What is the orange area?

Categories
Beginner

Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

Categories
Intermediate

Pentagon divided

Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. But you may divide a segment into a number of equal segments for free.)

Categories
Advanced

Squaring a rectangle II

A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.

Categories
Advanced

Crashing the kite

The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?

Categories
Intermediate

No laughing matter

Two squares share a vertex. Each square contains a coloured rectangle with extended side. What’s green : blue? By Matthew Arcus.

Categories
Intermediate

Playing fields

Show equality of the green and orange square playing field areas.

Categories
Intermediate

Vanishing point II

Six squares and four coloured triangles. What is red : blue : yellow : green?

Categories
Intermediate

Mind the steps

Three similar rectangles and a line segment. Express red in terms of blue and green.