There are a number of solid (three-dimensional) shapes studied in geometry. Prism is one of the most useful ones. A prism may be defined as a 3D shape having two bases in the shape of a polygon. Both bases are connected with each other with the help of rectangular or parallelogram-shaped lateral faces. A right prism has same cross section throughout and the line joining centers of both bases is perpendicular to them. The prisms are named after the polygonal bases they have. The following diagram demonstrates triangular and rectangular right prisms.

Related Calculators | |

Prism Surface Area Calculator | Calculate Surface Area of Rectangular Prism |

Surface Area of a Triangular Prism Calculator | Area of a Trapezoid Calculator |

A trapezoidal prism consists of two opposite faces or bases in the shape of trapeziums or trapezoids. Recall that a trapezoid is a plane figure having one pair of opposite sides to be parallel. The distance between parallel sides is known as the height of the trapezium. It is shown below :

Any trapezoidal prism is made up of 6 faces (2 bases and 4 lateral surfaces), 12 edges and 8 vertices. In a right trapezoidal prism, the opposite trapezoid-shaped bases are congruent and are connected together by the means of four rectangles. The diagram of a right trapezoidal prism is given as under :

There are two forms of surface areas of solid shapes - lateral surface area and total surface area. Let us suppose that there be a right trapezoidal prism as shown in the figure below.Any trapezoidal prism is made up of 6 faces (2 bases and 4 lateral surfaces), 12 edges and 8 vertices. In a right trapezoidal prism, the opposite trapezoid-shaped bases are congruent and are connected together by the means of four rectangles. The diagram of a right trapezoidal prism is given as under :

It includes the surface area of the lateral side of a prism. The formula for lateral surface area of the trapezoidal prism is given by :

LSA = Perimeter of base $\times$ height of prism

LSA = (a + b + c + d) $\times$ H

where, c and d be the length of non-parallel sides of the base.

It includes surface area lateral sides as well as the bases. The formula for total surface area will eventually be written as :

TSA = LSA + 2 $\times$ Area of base

or

TSA = (a + b + c + d) H + 2 $\frac{a+b}{2}$ h

or

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

For calculating the surface area, the following steps can be adopted.

Step 3 :

Step 1 :

Step 2 :

Step 3 :

Step 4 :

a = 4 cm, b = 10 cm, c = 3 cm = d

Height of the trapezoidal base, h = 2 cm

Perimeter of base, P = 4 + 10 + 3 + 3 = 20 cm

Height of the prism, H = 7 cm

Area of base = $\frac{a + b}{2}$ $\times\ h$ = $\frac{14}{2}$ $\times\ 2$ = 14 sq cm

Total surface area = Lateral surface area + 2 Area of base

Total surface area = (P $\times$ H) + 2 Area of base

= 20 $\times$ 7 + 2 $\times$ 14

= 140 + 28 = 168 sq cm.

Calculate its surface area.

Solution :

a = 5 cm, b = 8 cm, c = 6 cm , d = ?

For finding the fourth side, we use Pythagoras theorem in the right triangle

$d^{2} = (8 - 5)^{2} + 6^{2}$

$d^{2} = 3^{2} + 6^{2}$ = 9 + 36 = 45

d = $\sqrt{45}$ $\approx$ 6.7 cm

Perimeter of base, P = 5 + 8 + 6 + 6.7 = 25.7 cm

Height of the trapezoidal base, h = 6 cm

Height of the prism, H = 12 cm

Area of base = $\frac{a + b}{2}$ $\times\ h$ = $\frac{13}{2}$ $\times\ 6$

= 13 $\times$ 3 = 39 sq cm

Total surface area = Lateral surface area + 2 Area of base

Total surface area = (P $\times$ H) + 2 Area of base

= 25.7 $\times$ 12 + 2 $\times$ 39

= 308.4 + 78 = 386.4 sq cm.

Related Topics | |

Math Help Online | Online Math Tutor |