"Square Pyramid." From MathWorld-A Wolfram Web Resource. Other formulas for calculations are derived from the formulas above. Convert radians to degrees by multiplying θ by 180/π Since tan(θ) = side opposite θ / side adjacent θ we can say Cube The surface area, S, of a cube with edge, s, is: S 6s 2 Rectangular prism The surface area, S, of a rectangular prism is: S 2lw + 2lh + 2wh where l is the length, w is the width, and h is the height of the rectangular prism.We have another formula for θ in terms of the tangent from trigonometric ratios.Law of Sines we can say that s/sin(α) = h/sin(θ) Let's name theta θ = Side Face Angle and alpha α = the right angle (90°) formed by h and r.The angle of the pyramid side face is the angle formed between the side face and the base.r = a/2 and this is the run as it forms a right angle where r meets h at the center of the base.For the line s the rise is h = height of the pyramid.We know that the slope of a line is m = rise/run The total surface area of a pyramid is obtained by adding the area of all its faces (both the base and the side faces).To find the pyramid slope of the side face we want to calculate the slope of the line s = slant height.Squaring the 2 to get it back inside the radical,īase Surface Area of a square pyramid ( square).Units: Units are shown for convenience but do not affect calculations. Height is calculated from known volume or lateral surface area. Surface area calculations include top, bottom, lateral sides and total surface area. L = 4 x (1/2)as = 2as = 2a√(h 2 + (1/4)a 2) This calculator finds the volume, surface area and height of a triangular prism.Our base is side length a and for this calculation our height for the triangle is slant height s. For the isosceles triangle Area = (1/2)Base x Height.Lateral Surface Area of a square pyramid (× 4 isosceles triangles) This is also the height of a triangle side.By the pythagorean theorem we know that.Square Pyramid Formulas derived in terms of side length = a and height = h: Volume of a Square Pyramid Calculations are based on algebraic manipulation of these standard formulas. This will show as a result if you are using values that just do not make sense as reasonable values for a pyramid.īelow are the standard formulas for a pyramid. For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm 3, L in mm 2, B in mm 2 and A in mm 2. The units are in place to give an indication of the order of the results such as ft, ft 2 or ft 3.
Units: Note that units are shown for convenience but do not affect the calculations. In other words the point at the top of the pyramid is directly above the center point of the square base. This is also a right square pyramid where "right" refers to the fact that the apex lies directly above the centroid of the base. It is a regular pyramid since it has a square base which is a regular polygon. The square pyramid is a special case of a pyramid where the base is square. This online calculator will calculate the various properties of a square pyramid given 2 known variables.
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