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Semicircle

✨ The curved bridge

A semicircle is a two-dimensional shape formed by half of a circle. It is obtained when a circle is divided into two equal parts by a straight line passing through its center. Each part has a curved edge, which is half of the original circle's circumference, and a straight edge called the diameter. The two endpoints of the diameter are also the endpoints of the curved part.

Like a circle, a semicircle can be described using a radius, which is the distance from its center to any point on the original circle. The diameter is twice the radius. Although a semicircle has a curved boundary, it is not a circle because part of its boundary is a straight line. Semicircles appear in many familiar objects and designs, including arches, decorative patterns, measuring instruments and some road signs.

In mathematics, several useful properties can be calculated from the radius. The length of the curved part is half the circumference of the corresponding circle, so it equals π × r. If the straight diameter is included, the total perimeter of the semicircle is π × r + 2r. Its area is exactly half the area of the full circle, giving the formula (π × r²) ÷ 2.

For example, when the radius is 4 centimeters, the area is 8π square centimeters. A semicircle also has one line of symmetry: the line that passes through the center and is perpendicular to the diameter. This simple shape helps illustrate important ideas about circles, lengths, areas and symmetry.

💡 Did you know?

Did you know that the rainbow we see in the sky is a magnificent semicircle? But wait, it's a magic trick of nature! If you could fly very high in a plane, you would see that the rainbow is actually a complete circle. It's the Earth's ground that hides half of it from us!

In your schoolbag, you surely have a tool called a protractor. It almost always has the shape of a semicircle. Schoolchildren use it to measure angles. It goes from 0 to 180 degrees. It's the essential tool to become a little geometry genius!

The Romans often used the semicircle to build their theaters. Thanks to this shape, the sound of the actors' voices bounced off the walls and arrived perfectly at the ears of all spectators, even those sitting at the very end. It's a shape that knows how to 'listen' very well!