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2. Annulus (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Annulus_(mathematics)

   As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4 The area of an annulus is determined by the length of the longest line segment within the annulus, which is the chord tangent to the inner circle, 2 d in the accompanying diagram.

3. Similarity (geometry) - Wikipedia

   en.wikipedia.org/wiki/Similarity_(geometry)

   Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.

4. Pythagorean theorem - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_theorem

   A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram. [6] The triangles are similar with area , while the small square has side b − a and area (b − a) 2. The area of the large square is therefore

5. Surface area - Wikipedia

   en.wikipedia.org/wiki/Surface_area

   A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...

6. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. [ 1 ] More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry , i.e., a combination of rigid motions , namely a ...

7. Tetrahedron - Wikipedia

   en.wikipedia.org/wiki/Tetrahedron

   Its surface area is four times the area of an equilateral triangle: = =. [7] Its volume can be ascertained similarly as the other pyramids, one-third of the base times height. Because the base is an equilateral, it is: [ 7 ] V = 1 3 ⋅ ( 3 4 a 2 ) ⋅ 6 3 a = a 3 6 2 ≈ 0.118 a 3 . {\displaystyle V={\frac {1}{3}}\cdot \left({\frac {\sqrt {3 ...