Semicircle
an arc with endpoints that are the endpoints of a diameter
A semicircle is a two-dimensional shape that is a part of a circle. It is formed by taking a circle and dividing it into two equal halves along its diameter. The term semi means half, so a semicircle is literally half of a circle.
A semicircle has only one curved edge, which is the arc of the circle that forms the semicircle. The straight line that divides the circle into two halves is called the diameter of the semicircle. The diameter of a semicircle is also its longest chord.
The area of a semicircle is given by the formula: A = (πr²)/2, where r is the radius of the circle that forms the semicircle. This formula is derived from the formula for the area of a full circle, which is A = πr². To find the perimeter of a semicircle, we need to add the length of the diameter (2r) to the length of the semicircle arc (πr). Therefore, the perimeter of a semicircle is P = 2r + πr = (2 + π)r.
Semicircles are commonly used in many applications, such as in architecture, engineering, and mathematics. They can be found in the design of arches, domes, and circular windows. Semicircles are also used in geometry to help students understand concepts such as diameter, chord, circumference, arc length, and sector area.
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