![]() Step 5: Put the values in the formula, 2B + Lateral Surface Area(PH), to get the total surface area of the hexagonal prism.Įxample: Determine the total surface area of the trapezoidal prism.Find the base area B by putting the above values in the formula, (b1+b2)h/2 Step 4: Identify b1 and b2 (lengths of the bases) of the trapezoid and h (height) of the trapezoid.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. The surface area of the prism is 2 0 4 u n i t .Derivation of Surface Area of Trapezoidal Prism Where □ and □ are its two parallel sides and ℎ its height. Let us work out the area of the base of the prism. We can of course work out the area of each rectangular face individually and sum up all together we find the same result. Its area is given by multiplying its length by its width. We clearly see on the net that they form a large rectangle of length the perimeter of the base and width the height of the prism, The lateral surface area of the prism is the area of all its rectangular faces that join the two bases. Rectangle whose dimensions are the height of the prism and the perimeter of the prism’s base. The surface area of a prism: on the net of a prism, all its lateral faces form a large In the previous example, we have found an important result that can be used when we work out The surface area of the prism is 7 6 u n i t . t o t a l b a s e l a t e r a l u n i t To find the total surface area of the prism, we simply need to add two times the area of theīase (because there are two bases) to the lateral area. We do find the same area however we compose rectangles to make the base. We can of course check that we find the same area with adding the area of two rectangles Or as the rectangle of length 5 and width 4 from which the rectangle of length The base can be seen as made of two rectangles, We need to find the area of the two bases. Prism, which is given by multiplying its length by its width: Now, we can work out the area of the large rectangle formed by all the lateral faces of the The missing lengths can be easily found given that all angles in the bases are right angles. The width of the rectangle formed by all lateral faces is actually the perimeter of the base. Where □ and □ are the two missing sides of the base of the prism. They form a large rectangle of length 3 and width We see that all the rectangles have the same length: it is the height of the prism, On the net, the rectangular faces between the two bases are clearly to be seen.
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