Therefore, the lateral surface area of the pentagonal prism is 1500 sq units and the total surface area of the pentagonal prism is 3000 sq units.įAQs on Surface Area of Pentagonal Prism What is the Total Surface Area of a Pentagonal Prism in Geometry?
Thus, the lateral surface area of pentagonal prism = 5bh = 5 × 20 × 15 = 1500 sq units Given that: base length = 20 units, apothem length = 15 units, and height =15 units. Solution: As we know, the total surface area of the pentagonal prism is 5ab + 5bh, and the lateral surface area of a pentagonal prism is 5bh. Therefore, the total surface area of the pentagonal prism, TSA = 5ab + 5bhĮxample: Find the total surface area of the pentagonal prism and lateral surface area of the pentagonal whose base length is given as 20 units, apothem length is 15 units and height is 15 units. ⇒ Total surface area of pentagonal prism = 5ab + 5bh The total surface area of pentagonal prism = 5 × area of the base of pentagonal prism + lateral surface area of the pentagonal prism Therefore, the lateral surface area of the pentagonal prism, LSA = 5b × h = 5bh Thus, the lateral surface area of a pentagonal prism can be given by finding the perimeter of the base of the prism multiplied by its height. In general, the lateral surface area of a prism is equal to five times the product of its base and height. In order to determine we cut the pentagonal prism into its net and open it. Let us take a pentagonal prism, apothem length of the prism is "a", the base length of the prism is "b", and height of the prism is "h. Thus, the perpendicular drawn from one vertex of one base to the other base of the prism will be taken as its height.ĭerivation of Surface Area of Pentagonal Prism In the case of an oblique pentagonal prism, the bases are not perpendicular to each other.In the case of a right pentagonal prism, the bases are perpendicular to each other.
In the case of a regular pentagonal prism, both the pentagonal sides are of equal length, and the five rectangular sides with bases being perpendicular to each other.The pentagonal prism formula for calculating surface area remains the same for all kinds of pentagonal prisms. Lateral Surface Area, L = Ph = 5bh sq.If the apothem length of the prism is "a", the base length of the prism is "b" and the height of the prism is "h", the surface area of a pentagonal prism is given as: The surface area of a pentagonal prism gives the area of each face of the prism. A pentagonal prism has two kinds of surface area:
Oblique pentagonal prisms: The pentagon faces of a pentagonal prism are not exactly aligned on each other and the rectangular faces are not perpendicular to the pentagon faces.įormula of Surface Area of Pentagonal PrismĪs a pentagonal prism has a lateral surface, thus we can express its lateral surface area as well as total surface area.Right pentagonal prisms: A right pentagonal prism has congruent and parallel pentagonal faces and rectangular faces are perpendicular to the pentagon faces.In other words, a regular pentagonal prism has congruent rectangular faces. Regular pentagonal prisms: A regular pentagonal prism is a pentagonal prism whose bases have all sides equal, the side faces are rectangles, and the angles between the sides of the base are 108 degrees.We can classify pentagonal prisms on the basis of their rectangular and pentagonal faces. A pentagonal prism has 15 edges, 10 vertices, and 7 faces (2 pentagonal and 5 rectangular). Since it has a flat base, thus it has a total surface area as well as a curved/lateral surface area. The space occupied by the surface of a pentagonal prism is known as the surface area of a pentagonal prism. What is the Surface Area of Pentagonal Prism?
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