Table of Content

• What is a Trapezoid Prism?
• Trapezoidal Prism Definition
• Trapezoidal Prism Faces, Edges And Vertices
• Properties of Trapezoidal Prism
• Cross-Section of Trapezoid Prism
• Trapezoidal Prism Net
• Trapezoid Prism Volume
• Trapezoidal Prism Surface Area
• Trapezoid Prism Formulas
• FAQs

Properties of Trapezoidal Prism

Below listed are the properties of Trapezoidal Prism:

• Trapezoid Prisms have parallel trapezoidal bases
• They have rectangular faces
• Trapezoid Prisms have equal edge lengths connecting corresponding vertices.

Cross-Section of Trapezoid Prism

Cross-section of a Trapezoidal Prism exhibits a trapezoidal shape, providing a visual representation of the prism’s unique base structure. Trapezoid Prism structure is made of a polyhedron with two parallel trapezoidal bases and rectangular faces connecting the corresponding sides of the bases. The cross-section of a Trapezoid Prism reveals a trapezoidal shape showcasing the distinct features of its base.

Trapezoidal Prism Net

The net of a Trapezoid Prism unfolds into trapezoidal and rectangular sections showcasing how the prism can be flattened into a 2D representation. The three-dimensional geometric figure of Trapezoidal Prism is flattened into 2D highlighting the two parallel trapezoidal bases and rectangular faces connecting the corresponding sides.

Shape of a Trapezoid Prism

The trapezoidal shape of the base influences the appearance of the Trapezoid Prism distinguishing it from other geometric solids. The shape of a trapezoid prism includes two parallel trapezoidal bases. Connecting the corresponding sides of the trapezoids are rectangular or parallelogram faces. Also, the connecting faces are perpendicular to the bases forming a solid and closed structure. Thus, it will give Trapezoidal Prism a three-dimensional geometric figure with two parallel trapezoidal bases and rectangular faces connecting the corresponding sides.

Construction of Trapezoid Prism

To construct a Trapezoidal Prism, draw the trapezoidal base on a plane, extend its sides to create the prism’s height and connect corresponding vertices to form rectangular faces. Below are the construction steps of trapezoid prism :

Step 1. Draw the Trapezoidal Base: Sketch a trapezoid on a plane so that its sides and angles align with the desired dimensions.

Step 2. Extend the Sides: Extend lines from each trapezoidal side to create the prism’s height.

Step 3. Connect Corresponding Vertices: Join the corresponding vertices of the trapezoidal bases to form rectangular faces.

Applications of Trapezoid Prism

Trapezoid prisms find application in various fields, including: Architecture, Engineering, Geometry Education, Optics etc. Below listed are the applications of Trapezoid Prism:

• Architecture: Used in the design of buildings and structures.
• Engineering: Employed for creating components in machinery.
• Geometry Education: A useful example for teaching 3D geometry concepts.
• Optics: Applied in the design of optical devices.

Trapezoid Prism Volume

Trapezoid Volume Formula is given as:

V = 1/2 × (a+b) × h × l

Where

• a and b are the lengths of the trapezoidal bases,
• h is the height,
• l is the slant height.

Example: Find the Volume of Trapezoid when the bases are 4 cm and 3 cm, height is 6 cm and slant height is 8 cm then calculate the volume of trapezoid prism.

Solution:

• h = 6cm (height)
• a = 4cm (length of the longer base)
• b = 3cm (length of the shorter base)
• l = 8cm (slant height).

Volume (V) of trapezoid prism is calculated by formula:

V = 1/2 × (a+b) × h × l

Substitute values in the above formula, we get:

V = 1/2 × (4+3)cm × 6cm × 8cm

⇒ V = 168 cm³

Trapezoidal Prism Surface Area

Like every 3D shape, Trapezoid Prism has two types of surface areas:

• Lateral Surface Area of Trapezoid Prism
• Total Surface Area of Trapezoid Prism

Lateral Surface Area of Trapezoid Prism

Lateral surface area of trapezoid prism is given by:

LSA = (a + b + c + d) × H

where a, b, c, d are the lengths of the trapezoidal bases and h is the height.

Example: Given H = 6 meter and the sides of trapezoidal are a = 4m, b = 3m, c = 5m and d = 8m then find the LSA of the trapezoid prism.

Solution:

Lateral Surface Area (LSA) of trapezoid prism is calculated by formula:

LSA = (a + b + c + d) × H

Substitute values in the above formula, we get:

LSA = (4 + 3 + 5 + 8) m × H

⇒ LSA = (4 + 3 + 5 + 8) m × H

⇒ LSA = 20 m × (6)m

⇒ LSA = 120 m²

Total Surface Area of Trapezoid Prism

Total surface area of trapezoid prism is given by:

TSA = h (b + d) + l (a + b + c + d)

where a, b, c, d are the lengths of the trapezoidal bases, h is the height and l is the slant height.

Example: Given height = 5m, slant height = 10m and the sides of trapezoidal are a = 4m, b = 6m, c = 5m and d = 8m then find the TSA of the trapezoidal prism. Then Calculate the Total Surface Area (TSA) of trapezoid prism.

Solution:

Total Surface Area (SA) of trapezoid prism is calculated by formula:

TSA = h (b + d) + l (a + b + c + d)

Substitute values in the above formula, we get:

TSA = h (6m + 4m) + l (4m + 6m + 5m + 8m)

⇒ TSA = h×(10m) + l×(23m)

⇒ TSA = 5m × (10m) + 10m × (23m)

⇒ TSA = 50m² + 230m²

⇒ TSA = 280m²

Also Read,

• Octagonal Prism
• Surface Area of Prism
• Hexagonal Prism

Trapezoid Prism Formulas

The Trapezoid Prism formula includes