The given prism has two triangular bases. Let us calculate the surface area of the triangular prism given below with a base "b", the height of prism "h", and length "L".
Surface area of octagonal prism = 4a 2 (1 + √2) + 8aHĬheck out types of prisms to get more details about various prisms. Surface area of regular hexagonal prism = 6ah + 3√3a 2 Surface area of hexagonal prism = 6b(a + h) Surface area of pentagonal prism = 5ab + 5bh Surface area of trapezoidal prism = h (b + d) + l (a + b + c + d) Surface area of rectangular prism = 2(lb + bh + lh) Surface area of square prism = 2a 2 + 4ah Surface area of triangular prism = bh + (s1 + s2 + b)H Surface Area of Prism = (2 × Base Area) + (Base perimeter × height) See the table below to understand this concept behind the surface area of various prism: Shape The bases of different types of prisms are different so are the formulas to determine the surface area of the prism. The total surface area of a Prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height). Thus, the lateral surface area of prism = base perimeter × height The lateral area is the area of the vertical faces, in case a prism has its bases facing up and down. Let us look at the surface area of the prism formula The total surface area of a prism is the sum of lateral surface area and area of two flat bases. To find the surface area of any kind of prism we use the general formula. Finding the surface area of a prism means calculating the total space occupied by all the faces of that respective type of prism or the sum of the areas of all faces (or surfaces) in a 3D plane. The surface area of the prism is 2 0 4 u n i t .The surface area of a prism refers to the amount of total space occupied by the flat faces of the prism. Where 𝑎 and 𝑏 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 𝑎 and 𝑏 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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