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The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by r 2 + h 2 {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where r {\displaystyle r} is the radius of the base and h {\displaystyle h} is the height.
The slant height of a right square pyramid is defined as the height of one of its isosceles triangles. It can be obtained via the Pythagorean theorem : s = b 2 − l 2 4 , {\displaystyle s={\sqrt {b^{2}-{\frac {l^{2}}{4}}}},} where l {\displaystyle l} is the length of the triangle's base, also one of the square's edges, and b {\displaystyle b ...
The pyramid's height is the distance of the peak from the plane. This construction gets generalized to n dimensions. The base becomes a (n − 1)-polytope in a (n − 1)-dimensional hyperplane. A point called the apex is located outside the hyperplane and gets connected to all the vertices of the polytope and the distance of the apex from the ...
1.2 Chord length and height. 1.3 Arc length ... θ the central angle subtending the arc ... the area is one quarter the circle when θ ~ 2.31 radians (132.3°) ...
Half-hipped (clipped gable, jerkinhead [7]): A combination of a gable and a hip roof (pitched roof without changes to the walls) with the hipped part at the top and the gable section lower down. Dutch gable, gablet : A hybrid of hipped and gable with the gable (wall) at the top and hipped lower down; i.e. the opposite arrangement to the half ...
Greek: the ridge height is 1 ⁄ 9 to 1 ⁄ 7 the span (an angle of 12.5° to 16°); Roman: the ridge height is 2 ⁄ 9 to 1 ⁄ 3 the span (an angle of 24° to 34°); Common: the rafter length is 3 ⁄ 4 the span (about 48°); Gothic: the rafters equal the span (60°); and; Elizabethan: the rafters are longer than the span (more than 60°). [7]
Whether you're heading home after the holidays or have festive plans to celebrate New Years Day, the busy holiday travel period continues, and weather may be a factor.
By using the identity a 3 − b 3 = (a − b)(a 2 + ab + b 2), one gets: = + +, where h 1 − h 2 = h is the height of the frustum. Distributing and substituting from its definition, the Heronian mean of areas B 1 and B 2 is obtained: