Total surface area of a trapezoidal prism12/28/2023 ![]() 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, The total surface area formula for a hexagonal prism is given as:Ĭalculate the total surface area of an isosceles trapezoid whose parallel sides of the base are 50 mm and 120 mm and legs of the base are 45 mm each, the height of the base is 40 mm, and the height of the prism is 150 mm.On the net, the rectangular faces between the two bases are clearly to be seen. Thus, the cost of painting the rectangular prism is $3,600įind the total surface area of a hexagonal prism whose apothem length, base length, and height are given as 7 m, 11 m, and 16 m, respectively. The total cost of painting the prism = TSA x cost of painting Surface area of a rectangular prism = 2h (l +b) If the painting cost is $50 per square inch, find the total cost of painting all faces of the prism.įirst, calculate the total surface area of the prism Thus, the total surface area of the pentagonal prism is 1885 cm 2Ī rectangular prism of dimensions, length = 7 in, width = 5 in and height = 3 in is to be painted. The formula for the total surface area of a pentagonal prism is given by Find the total surface area of the pentagonal prism. The apothem length, base length, and height of a pentagonal prism are 10 cm. Hence, the total surface area of the prism is 343.44 cm 2. Thus, the apothem length of the prism is 6.93 cm ![]() The base is an equilateral triangle of side 8 cm.īy Pythagorean theorem, the apothem length, a of the prism is calculated as: Therefore, the total surface area of the triangular prism is 240 cm 2.įind the total surface area of a prism whose base is an equilateral triangle of side 8 cm and height of the prism is 12 cm. Now substitute the base area, height, and perimeter in the formula. Since the base is a triangle, then the base area, B =1/2 ba TSA = 2 x area of the base + perimeter of the base x Height The other two sides of the triangular base are 7 cm each.įind the total surface area of the triangular prism. The dimensions of a triangular prism are given as follows: Let’s solve a few example problems involving the surface area of different types of prisms. Note: The formula to find the base area (B) of a prism depends on the base’s shape. Where TSA = Total surface area of a prism Total surface area of a prism = 2 x area of the base + perimeter of the base x Height ![]() Therefore, the surface area of a prism formula is given as: Since we know the total surface area of a prism is equal to the sum of all its faces, i.e., the floor, walls, and roof of a prism.
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