The large base is #HJ# which consists of three segments: Since we have to find an expression for #V#, the volume of the water in the trough, that would be valid for any depth of water #d#, first we need to find an expression for the large base of trapezoid #CDHJ# in terms of #d# and use it to calculate the area of the trapezoid. The volume of water is calculated by multiplying the area of trapezoid #CDHJ# by the length of the trough. This change affects the length of the large base of the trapezoids at both ends. Thats all The general formula for a regular octagonal pyramid reads: V 2 × (1 + 2) / 3 × a² × h. The water in the trough forms a smaller trapezoidal prism whose length is the same as the length of the trough.īut the trapezoids in the front and the back of the water prism are smaller than those of the trough itself because the depth of the water #d# is smaller than the depth of the trough.Īs the water level varies in the trough, #d# changes. To get the volume of a regular octagonal pyramid with a side length of a and a height of h: Square the side length to get a². The water level in the trough is shown by blue lines. The volume of prism is calculated by multiplying the area of the trapezoid #ABCD# by the length of the trough.īut we are asked to figure out the volume of the water in the trough, and the trough is not full. The trough itself is a trapezoidal prism. Trapezoidal footing is formed by combining cuboid.

Calculations and graphs may be performed in Excel, Google Sheets, or on a TI-Nspire calculator. The constructed container should be decorated as it were a real chocolate bar. In other words, multiply together the length, height, and average of A and B. The container has be a trapezoidal prism, and the trapezoidal face must be an isosceles trapezoid that contains acute angles of 60 degrees. Here is another derivation of the area formula for a trapezium. This can be thought of as ‘the height times the average of the parallel sides’. The front and back of the trough are isosceles trapezoids. If the prism length is L, the trapezoid base width is B, the trapezoid top width is A, and the trapezoid height is H, then the volume of the prism is given by the four-variable formula: V (L, B, A, H) LH (A + B)/2. So the formula for the area of a trapezium with parallel sides a and b and the perpendicular distance h between them is. The figure above shows the trough described in the problem.

Volume of a trapezoidal prism excel