![]() Step 3: Put the values in the formula, (a+b+c+d) × H or PH, to find the lateral surface area of the hexagonal prism.Step 2: Identify the length H of the prism.Add these 4 values in order to find the perimeter P. Step 1: Identify the four sides of the trapezium - a, b, c, and d, representing the widths of the four rectangles.Note that all measurements are of the same units. Here are the steps to calculate the surface area of a trapezoidal prism. How to Calculate the Surface Area of a Trapezoidal Prism? Thus, the total surface area of a trapezoidal prism is h(b+d)+l(a+b+c+d) square units. TSA of the trapezoidal prism = h (b + d) + l (a + b + c + d). Therefore, the total surface area of the trapezoidal prism (TSA) = 2 × h (b + d)/2 + (a × l)+(b × l) + (c × l) + (d × l) = h (b + d) + Substituting the values from equation (2) and equation (3) in the TSA formula, which is represented by equation (1): The lateral surface area of the trapezoidal prism (LSA) is the sum of the areas of each rectangular surface around the base that means, LSA = (a × l) + (b × l) + (c × l) + (d × l) - (3) Thus, the area of trapezoidal base = h (b + d)/2 - (2) We already know that the total surface area of the trapezoidal prism (TSA) = 2 × area of base + lateral surface area - (1)Īlso, the area of a trapezoid = height(base1 × base 2)/2. l is the length of the trapezoidal prism.h is the distance between the parallel sides.We know that the base of a prism is in the shape of a trapezoid. All the other cases can be calculated with our triangular prism calculator.Derivation of Surface Area of Trapezoidal Prism ![]() The only case when we can't calculate triangular prism area is when the area of the triangular base and the length of the prism are given (do you know why? Think about it for a moment). Using law of sines, we can find the two sides of the triangular base:Īrea = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2) Triangular base: given two angles and a side between them (ASA) Using law of cosines, we can find the third triangle side:Īrea = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle) Triangular base: given two sides and the angle between them (SAS) However, we don't always have the three sides given.
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