Birds, Bees and Burgers: Puzzling Geometry from EnigMaths

By Paulo Ferro

Problems are presented simply and colorfully, and solutions are well expounded and clear. The reader will enjoy the challenge, and the "aha" moment of understanding any solution that they did not come to themselves. Great fun—and enlightening, too!

• Language: English
• Publisher: Tarquin Group
• Release date: Aug 20, 2021
• ISBN: 9781913565596

Book preview

Level 1

The equilateral triangle is inscribed in a circle.

What fraction of the big circle is shaded?

The big square has side with length 5.

What is the area of the small square?

A regular pentagon is made with 5 congruent squares.

Find the missing angle.

A circle and a semicircle meet at the centre of a big circle with radius 4.

What is the total shaded area?

A regular hexagon is inside a rhombus such that two of its sides lie on the sides of the rhombus. The dots separate the side in 3 equal parts.

What fraction of the rhombus is shaded?

A circle and a semicircle are inside an equilateral triangle.

What is the area of the semicircle?

Two circles and a semicircle are inside a big circle. The second circle meet the semicircle at the centre of the big circle.

What is the area of the semicircle?

An equilateral triangle and a square meet at the centre of a circle.

What is the area of the equilateral triangle?

The points in each side are equally spaced.

What fraction of the square is shaded?

An equilateral triangle, a square and a regular hexagon have the same side length.

What is the size of the angle?

Solutions and Answers

1-1

Answer:

Let r be the radius of the circle inscribed in the equilateral triangle.

The circle where the equilateral triangle is inscribed has radius 2r.

Each of the three small circles have diameter 2r − r = r. So, their radii are

The area of the circle inscribed in the equilateral triangle is πr².

The area of each of the small