lateral surface area of a triangular prism

The volume of a truncated prism is given by the formula below. For a truncated regular prism, the right section is equal to the base area.

K is the area of the right section and L is the average length of the lateral edges. In general, the volume of a truncated prism is equal to the product of the area of its right section, and the average of the lengths of its lateral edges. The total surface area of a truncated prism is the sum of the areas of the two polygonal bases and the right trapezoidal faces. If the cut off prism is a right prism, then the lateral faces are right trapezoids. The lateral edges are non-congruent and the lateral faces are quadrilaterals (rectangles or trapezoids). Since the truncating plane is not parallel to the base, the solid formed has two nonparallel bases, which are both polygons of the same number of edges. The total surface area of a prism or a pyramid can thus be determined in terms of the area of its various faces.A truncated prism is a portion of a prism formed by passing a plane not parallel to the base and intersecting all the lateral edges. = 4 x the area of each equilateral triangular face. The total area of the bases = 2 x the area of each equilateral triangular surface.Ĭase III – The total surface area of the regular tetrahedron (Figure 34.2) ∴ the total surface area = total lateral surface area + total area of the bases.Ĭase II – The total lateral surface area of the prism = 3 x the area of each rectangular face. The total area of the bases = 2 x the area of each equilateral triangular face. area length (a + b + c) + (2 basearea), where a, b, c are sides of the. The two most basic equations are: volume 0.5 b h length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length. Step 6: All the four faces are congruent equilateral triangles and the sum of the areas of these triangles will give the total area of the tetrahedron (see Calculations, Case III).Ĭase I – The total lateral surface area of the prism = 3 x area of each square face. Usually what you need to calculate are the triangular prism volume and its surface area. Step 5: Cut the model of the regular tetrahedron (right-triangular pyramid) shown in Figure 34.2 along its edges and open it up to obtain a figure of the form shown in Figure 34.4. The total surface area of the prism is therefore the total area of all the five faces (see Calculations, Case II). Step 4: The two faces forming the bases are congruent equilateral triangles and the three faces forming the lateral surfaces are congruent rectangles. Step 3: Cut the model of the right-triangular prism shown in Figure 34.1(b) along its edges and open it up to obtain a figure of the form shown in Figure 34.3(b). The total surface area of the prism is therefore the total area of all the five faces (see Calculations, Case I).

Step 2: The two faces forming the bases are congruent equilateral triangles and the three faces forming the lateral surfaces are congruent squares. Step 1: Cut (using the cutter) the model of the right-triangular prism shown in Figure 34.1(a) along its edges and open it up to obtain a figure of the form as shown in Figure 34.3(a). A regular tetrahedron is shown in Figure 34.2. The right-triangular pyramid (also called the regular tetrahedron) has four congruent equilateral triangles, out of which any one forms the base and the remaining ones form the lateral surfaces. Type II – It has two congruent equilateral triangles as bases and three congruent rectangles forming the lateral surfaces. Type I – It has two congruent equilateral triangles as bases and three congruent squares forming the lateral surfaces. There are two types of right-triangular prisms: Cardboard models of a right-triangular prism and a right-triangular pyramid.a right-triangular pyramid (a regular tetrahedron).Math Labs with Activity – Determine the Total Surface Area

Lateral surface area of a triangular prism