#Find surface area of hexagonal prism how to#

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. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.And then calculate the area of lateral faces connecting the bases.To find the total surface area of a prism, you need to calculate the area of two polygonal bases, i.e., the top face and bottom face.In a prism, the lateral faces, which are parallelograms, are perpendicular to the polygonal bases. A prism is named according to the shape of the polygonal bases. To recall, a prism is a 3-dimensional polyhedron with two parallel and congruent bases, which are connected by lateral faces.

#Find surface area of hexagonal prism how to#

In this article, you will learn how to find the total surface area of a prism by using the surface area of a prism formula. The total surface area of a prism is the sum of areas of its lateral faces and its two bases. The surface area of the prism is 2 0 4 u n i t .Surface Area of a Prism – Explanation & Examples 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.