Square Prism Definition – Let’s begin with the background information needed to understand the topic of the surface area of a square prism. A square prism (right square prism) is a prism with four sides like a rectangle and two squares as its bases (one square acts as the top). It is also known as a square cuboid or square box. It is a four-sided prism whose base and vertex are equal squares and the remaining 4 sides are rectangles. Both squares are parallel and equal to each other. Rectangles are also compatible with each other.
The surface area of a square prism is the total area covered by the surface of the square prism. A square prism has four rectangular sides and two square bases. The surface area of a square prism is expressed in square units, common units are square meters, square centimeters, square inches, etc. Like other three-dimensional shapes, a square prism has two types of area,
Square Prism Definition
In the next section, let us understand the formulas for calculating the lateral area and total surface area of a square prism.
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The surface area of a square prism is the sum of the areas of its faces and its bases. We know that a square prism is:
Therefore, the surface area of a square prism is the sum of the areas of its four rectangular lateral faces and the area of the base, which are squares.
For a square prism, if the length of the side of the square base is given, then the area of the base can be given by,
For a square prism, if the length of the side of the square and the height of the prism are given, then its lateral surface area is,
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Square prism = Area of four rectangular sides | Since the 4 rectangles are congruent, their areas will be equal.
Surface area of a square prism = 4 × (s × h) = 4sh, where s is the side length of the square and h is the height of the square prism.
For a square prism, if the length of the side of the square and the height of the prism are given, its total surface area can be given as:-
+ 4sh, where s is the side length of the square and h is the height of the square prism.
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+ 4sh and the lateral surface area is squared in 4sh units. Now that we have seen the formula and method for calculating the surface area of a square prism, let’s look at some worked examples to understand it better.
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The surface area of a square prism is the area or area covered by the surfaces of the three-dimensional figure. A square prism has 2 square bases and 4 rectangular sides. A square prism consists of two types of area: lateral surface area and total surface area.
The formula used to calculate the total surface area of a square prism is TSA of a square prism = 2 × s
File:pentagonal Prism (heptahedron).svg
+ 4sh, where s is the side length of the square and h is the height of the square prism. However, the formula for calculating the lateral surface area of a square prism is LSA of square prism = 4sh, where s is the side length of the square and h is the height of the square prism.
The lateral surface area of a square prism is the area covered by the lateral or lateral faces of the square prism. The surface area of a partition can be calculated using the given formula, LSA of a square prism = 4sh, where s is the side length of the square and h is the height of the square prism.
The total surface area of a square prism is expressed in square units. Common units used are square meters, square centimeters, square inches, square yards, etc.
The surface area of a square prism is given by the formula: TSA of a square prism = 2 × s
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+ 4sh, where s is the side length of the square and h is the height of the square prism. Given the surface area and side length of the base square, we can plug the given values into the formula and solve for the height.
The lateral surface area of a square prism is the area covered by the lateral or lateral surfaces, while the total surface area of a square prism is the area covered by all faces, including the two square bases. A prism is a solid three-dimensional object that has identical faces on both sides. Other faces are straight. A prism is named after its base. Therefore, they are named differently based on the shape of their base. Let’s learn more about the world of Prism!
A prism is an important member of the polyhedra family that has identical polyhedra at its base and vertex. The other faces of the prism are called lateral faces. This means that the prism does not have a curved face. A prism has the same cross section throughout its length. Prisms are placed according to their cross section. A metal nut is the best example to represent a hexagonal prism, a fish tank represents a rectangular prism, and many other living devices in our environment represent prisms.
Before reading about the different types of prisms, let us understand on what basis the types of prisms can be obtained. Prisms can be classified as follows:
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A prism is classified based on its type. There are two types of prisms in this category, called:
A prism is named after the shape obtained from the cross section of the prism. They are further classified:
There are two basic formulas that we study in geometry about all related three-dimensional shapes. The two formulas are the area of a shape and the volume of a shape. Let us study both of them in the form of prisms.
There are two types of areas that we study about, first, the lateral surface area of the prism, and second, the total surface area of the prism. Let’s learn in detail.
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The lateral area of a prism is the sum of the areas of all its lateral faces, while the total surface area of a prism is the sum of its lateral area and the area of its bases.
Total surface area of prism = lateral surface area of prism + area of two bases = (2 × base area) + lateral surface area or (2 × base area) + (circumference of base × height).
There are seven types of prisms that we read about above based on the shape of the bases. The bases of the different types of prisms are different, as are the formulas for determining the surface area of a prism. To understand the concept behind the surface area of different prisms please refer to the table below:
The volume of a prism is defined as the total volume of space or space that a prism occupies. The volume of a prism is the product of the area of the base and the height of the prism. Therefore, the volume of a prism is V = B × H, where “V” is the volume, “B” is the area of the base, and “H” is the height of the prism. Base area (Unit
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) and the height of the prism is given in (units). Therefore, the unit of volume of the prism is V = (unit
Volume of triangular prism = area of triangle × height of prism = ½ × b × h × l
Volume of trapezoidal prism = area of trapezoid × height of prism = ½ × (a + b) × h × h
Volume of pentagonal prism = area of pentagon × height of prism = (5/2) × a × b × h
Finding The Surface Area And Volume Of Frustums Of A Pyramid And Cone
Mathematics will no longer be a difficult subject, especially when you understand concepts through concepts.
Prisms are an important member of the polyhedra family. A prism has two identical faces which are named after them. It is a three-dimensional shape and can be classified as follows:
The cross section of a prism is the shape obtained by cutting the prism through an axis. The cut is made in a straight line with bases at right angles. In other words, a prism has a cross section of exactly the same shape and size throughout its length. For example, a triangular prism has a triangular cross section along its entire length from end to end.
A straight prism has two flat ends that are perfectly aligned, while an oblique prism appears flat and the two flat ends are not aligned. In a right prism, all the lateral faces are rectangles, while the faces of oblique prisms are parallelograms.
Volume Of Square Prism
A prism is a three-dimensional solid
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