Answer: Rectangular Prism
Rectangular prisms are three-dimensional shapes with six faces. The top, bottom, and lateral faces of a prism are all rectangles, and all pairs of opposing faces of the prism are congruent. Rectangular prism have surface area and volume, just like any other three-dimensional form. The term “cuboid” also applies to rectangular prisms.
Rectangular prism specifications include:
- Have three dimensions: height, width, and depth.
- Exhibit parallel, polygonal faces
- Take the shape of a hexahedron.
- Possess sides that are structured like a parallelogram; this is significant since it sets a rectangular prism apart from a triangular prism.
- Consist of 8 vertices and 12 edges.
Characteristics of a Rectangular Prism:
- Six rectangular faces, twelve sides, and eight vertices form a rectangular prism.
- A rectangular prism has congruent opposite sides on all of them.
- There is a rectangular cross-section in a rectangular prism.
- A straight line joining two sides defines a 3D shape’s edge.
- To make it easier for us to recognize particular edges or faces, you can label the vertices, or corners, of a rectangular prism.
Different Types of Rectangular Prism
Oblique and cuboid are the two types of rectangular prisms. Let’s know about them in brief.
- Oblique: The faces of an oblique rectangular prism are not parallel to the bases. To put it another way, this prism’s faces are parallelograms.
- Cuboid: A cuboid has equal and parallel opposing faces, and all of its angles are right angles. An alternative name for this three-dimensional structure is a right rectangular prism. It should be noted that not all cuboids are cubes, but cubes are cuboids. Refrigerators and aquariums are two real-world instances of right rectangular prisms/cuboids.
Volume and Surface Area of a Rectangular Prism
There are three dimensions to the rectangular prism. It indicates that it has a volume and a surface area.
The following formula can be used to determine a rectangular prism’s surface area as all of its sides are rectangles and its opposite faces are equal:
Total Surface Area: 2 (width x length) + (length x height) + (width x height)
Lateral Surface Area: 2 (length x height) + (width x height)
Multiplying each of the three dimensions gives the volume of a rectangular prism.
Formulas for Rectangular Prisms
We will now get the formulas for a rectangular prism’s surface area and volume. Let us assume a rectangular prism with dimensions of length ‘l’, width ‘w’, and height ‘h’ for each of these. Let’s assume that ‘l’ and ‘w’ represent the base’s measurements along these lines. The following are the formulas for a rectangular prism’s surface area and volume.
Volume, V = lwh
Total surface area = 2 (l+wh+hl)
Lateral surface area = 2 (wh+hl)
Rectangular Prism: Solved Examples
Example 1
Ques: Given a right rectangular prism with dimensions of 5 feet by 4 feet for width, 6 feet for height, and 4 feet for length, what is the total area?
Sol: Total surface area = 2 (WL) + (LH) + (WH)
2 (45) + (56) + (46)
2 (20) + (30) + (24)
148 ft2
Example 2
Ques: Find the lateral and total surface area of a rectangular prism with length 16 cm, width 12.5 cm, and height 10 cm.
Sol: Given what is known,
Lateral Surface Area (LSA) is equal to 2(wh + hl), where w = 12.5 cm, h = 10 cm, and l = 16 cm.
Therefore, LSA is equal to 2(12.5 × 10 + 10 × 16).
= 570 square centimeters.
The formula for Total Surface Area (TSA) is 2(lw + wh + hl), where l is 16 cm, w is 12.5 cm, and h is 10 cm.
∨ TSA = 2(16 × 12.5 + 12.5 × 10 + 10 × 16)
= 970 cm2
Example 3
Ques: Determine the volume of a rectangular prism using the following measurements: 7 cm for length, 6 cm for width, and 4 cm for height.
Sol: Given,
length, l = 7 cm.
breadth, w = 6 cm
Height: h = 4 cm
According to l.w.h., the volume of a rectangular prism
L x W x H is the cubic unit of V.
Enter the values for l, w, and h in the formula.
V is equivalent to 7 x 6 x 4 cm^.
Consequently, 168 cm³ is the volume of a rectangular prism.
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