# Volume & Surface Area of a Trapezoidal Prism

Trapezoidal prisms are three dimensional solids. They consist of two congruent trapezoids that are connected to each other by four rectangles. This lesson will include the definition and how to find the surface area and the volume of these solids.

Trapezoidal Prism Introduction

The term trapezoidal prism may not familiar to you. If you’ve ever noticed the shape of most circular fire-pit bricks, then you will be familiar with trapezoidal prisms. They look like a typical brick except one side is shorter than the other. This lesson is about describing a trapezoid and a trapezoidal prism. It will also cover the formulas for the surface area and volume of these prisms.

Trapezoids and Trapezoidal Prisms

Before we can talk about what a trapezoidal prism is, we need to know what a trapezoid is. Trapezoids are quadrilaterals (four sided figures) that have only one set of parallel lines. They are different from other types of quadrilaterals (parallelograms, rectangles, squares) that have two sets of parallel lines. The two sides of the trapezoid that are parallel are called bases, and they won’t be the same length. To find the surface area and volume of a trapezoidal prism, you will need to know the formula for finding the area of a trapezoid. The area of a trapezoid is h(b1+b2)/2, where b1 and b2 are the lengths of the two bases and h is the height of the trapezoid.

A trapezoidal prism is a three dimensional solid that has two congruent trapezoids for its top and lower base. It will have four rectangles that connect the corresponding sides of the two bases. These four rectangles are called the lateral faces of the prism.

How to Find the Surface Area

To find the surface area, the amount of space on the outside of a solid, of a trapezoidal prism, you’ll need to find the area of the trapezoid base and multiply it by two. You’ll then add the area of the four rectangles to the area of the two bases. The width of the four rectangles will be the same as the height of the prism. The length of the four rectangles will be the sum of the four sides of the trapezoid, the two bases, and the other two sides. The surface area can be given with this formula: Surface Area of Trapezoidal Prism = (b1+b2)h + PH. In this formula, b1 and b2 stand for the length of the bases of the trapezoid. Lower case h is the height of the trapezoid. Upper case P is the perimeter of the trapezoid, and upper case H is the height of the prism.

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