S = h (b + d) + l (a + b + c + d) Hence, the surface area of a trapezoidal prism is h(b+d)+l(a+b+c+d). S = h (b + d) + a × l + b × l + c × l + d × l The surface area of the trapezoidal prism (S) = 2 × h (b + d)/2 + (a × l)+(b × l) + (c × l) + (d × l) Put the values from equation (2) and equation (3) in equation (1): The lateral surface area of the trapezoidal prism = the sum of the areas of each rectangular surface around the base. The surface area of the trapezoidal prism (S) = 2 × area of base + lateral surface area - (1) We know that the base of a prism is in the shape of a trapezoid. Let's solve this question with the help of a given diagram of the trapezoidal prism. We will find the surface area of a trapezoidal prism in few steps. Answer: The surface area of a trapezoidal prism is h (b + d) + l (a + b + c + d) #GK#, in the middle, is equal to #DC# because #DE# and #CF# are drawn perpendicular to #GK# and #AB# which makes #CDGK # a rectangle.How to find the surface area of a trapezoidal prism?Ī trapezoidal prism is a three-dimensional solid made up of two trapezoids on opposite faces joined by four rectangles called the lateral faces. 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. 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. It has 24 edges and 16 vertices. The octagonal prism, is a figure formed by 10 faces, 2 of which are equal and parallel octagons, and form the bases at the ends of the shape.Another 8 faces are parallelograms. To find the volume of the isosceles trapezoidal prism, we need to first calculate the area of the trapezoid base and then multiply it by the height of the prism. Description, how many faces, edges and vertices are there in an octagonal prism. In this formula, 'b1' and 'b2' stand for the length of the bases of the trapezoid. The water level in the trough is shown by blue lines. The volume of the isosceles trapezoidal prism is 1575 cubic meters. The surface area of a trapezoidal prism can be given with this formula: (b1+b2)h + PH. 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. The base of a prism is always the trapezoid for a trapezoidal prism. The surface area can be given with this formula: Surface Area of Trapezoidal Prism Sa (l + h) + b (l + h) + lc + ld. One edge of the rectangle is the perimeter of the triangle. The length of the four rectangles will be the sum of the four sides of the trapezoid, the two bases, and the other two sides. Image caption, The rectangular faces can be combined to form one rectangle. The front and back of the trough are isosceles trapezoids. The total surface area of the prism is 96 cm. The figure above shows the trough described in the problem.
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